System, method, and apparatus for estimating liquid delivery

ABSTRACT

A pump includes a reservoir, a port, and a plunger. The reservoir delivers a liquid by discharging the liquid through the port coupled to the reservoir. A piston of the plunger defines a liquid side of the reservoir and a non-liquid side of the reservoir whereby movement of the plunger towards the liquid side of the reservoir discharges liquid through the port. The pump also includes a reference-volume assembly and/or a linear position sensor. The reference-volume assembly is coupled to the reservoir at an opposite end of the reservoir relative to the port and includes a reference-volume chamber in acoustic communication with the non-liquid side of the reservoir, a speaker disposed within the reference-volume chamber, and a reference microphone disposed within the reference-volume chamber. The pump estimate the amount of liquid discharged from the reservoir.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. patent application Ser. No.15/467,196, filed Mar. 23, 2017 and entitled System, Method, andApparatus for Estimating Liquid Delivery, now U.S. Publication No. US2017-0224909-A1, published Aug. 10, 2017 (Attorney Docket No. U91),which is a continuation of U.S. patent application Ser. No. 13/723,251,filed Dec. 21, 2012 and entitled System, Method, and Apparatus forEstimating Liquid Delivery, now U.S. Pat. No. 9,636,455, issued May 2,2017 (Attorney Docket No. J81) which is a Non-Provisional which claimspriority to and the benefit of the following:

U.S. Provisional Patent Application Ser. No. 61/578,649, filed Dec. 21,2011 and entitled System, Method, and Apparatus for Infusing Fluid(Attorney Docket No. J02);

U.S. Provisional Patent Application Ser. No. 61/578,658, filed Dec. 21,2011 and entitled System, Method and Apparatus for Estimating LiquidDelivery (Attorney Docket No. J04);

U.S. Provisional Patent Application Ser. No. 61/578,674, filed Dec. 21,2011 and entitled System, Method and Apparatus for Dispensing OralMedications (Attorney Docket No. J05);

U.S. Provisional Patent Application Ser. No. 61/651,322, filed May 24,2012 and entitled System, Method, and Apparatus for Electronic PatientCare (Attorney Docket No. J46); and

U.S. Provisional Patent Application Ser. No. 61/679,117, filed Aug. 3,2012 and entitled System, Method, and Apparatus for Monitoring,Regulating, or Controlling Fluid Flow (Attorney Docket No. J30), each ofwhich is hereby incorporated herein by reference in its entirety.

U.S. patent application Ser. No. 13/723,251, filed Dec. 21, 2012 andentitled System, Method, and Apparatus for Estimating Liquid Delivery,now U.S. Pat. No. 9,636,455, issued May 2, 2017 (Attorney Docket No.J81) claims priority to, benefit of, and is also a Continuation-In-Partapplication of the following:

U.S. patent application Ser. No. 13/333,574, filed Dec. 21, 2011 andentitled System, Method, and Apparatus for Electronic Patient Care, nowU.S. Publication No. US 2012-0185267-A1, published Jul. 19, 2012(Attorney Docket No. I97), and

PCT Application Serial No. PCT/US11/66588, filed Dec. 21, 2011 andentitled System, Method, and Apparatus for Electronic Patient Care(Attorney Docket No. I97WO), both of which are hereby incorporatedherein by reference in their entireties.

U.S. patent application Ser. No. 15/467,196, filed Mar. 23, 2017 andentitled System, Method, and Apparatus for Estimating Liquid Delivery,now U.S. Publication No. US 2017-0224909-A1, published Aug. 10, 2017(Attorney Docket No. U91) may also be related to one or more of thefollowing patent applications filed on even date herewith, all of whichare hereby incorporated herein by reference in their entireties:

U.S. patent application Ser. No. 13/723,238, filed Dec. 21, 2012 andentitled System, Method, and Apparatus for Clamping, now U.S. Pat. No.9,759,369, issued Sep. 12, 2017 (Attorney Docket No. J47);

U.S. patent application Ser. No. 13/723,235, filed Dec. 21, 2012, andentitled System, Method, and Apparatus for Dispensing Oral Medications,now U.S. Pat. No. 9,400,873, issued Jul. 26, 2016 (Attorney Docket No.J74);

PCT Application Serial No. PCT/US12/71131, filed Dec. 21, 2012 andentitled System, Method, and Apparatus for Dispensing Oral Medications(Attorney Docket No. J74WO);

U.S. patent application Ser. No. 13/724,568, filed Dec. 21, 2012 andentitled Syringe Pump, now U.S. Pat. No. 9,295,778, issued Mar. 29, 2016(Attorney Docket No. J75);

U.S. patent application Ser. No. 13/725,790, filed Dec. 21, 2012 andentitled System, Method, and Apparatus for Infusing Fluid, now U.S. Pat.No. 9,677,555, issued Jun. 13, 2017 (Attorney Docket No. J76);

PCT Application Serial No. PCT/US12/71490, filed Dec. 21, 2012 andentitled System, Method, and Apparatus for Infusing Fluid (AttorneyDocket No. J76WO);

U.S. patent application Ser. No. 13/723,239, filed Dec. 21, 2012 andentitled System, Method, and Apparatus for Electronic Patient Care, nowU.S. Pat. No. 10,108,785, issued Oct. 23, 2018 (Attorney Docket No.J77);

U.S. patent application Ser. No. 13/723,242, filed Dec. 21, 2012 andentitled System, Method, and Apparatus for Electronic Patient Care, nowU.S. Publication No. US 2013-0317753-A1, published Nov. 28, 2013(Attorney Docket No. J78);

U.S. patent application Ser. No. 13/723,244, filed Dec. 21, 2012 andentitled System, Method, and Apparatus for Monitoring, Regulating, orControlling Fluid Flow, now U.S. Pat. No. 9,151,646, issued Oct. 6, 2015(Attorney Docket No. J79);

PCT Application No. PCT/US12/71142, filed Dec. 21, 2012 and entitledSystem, Method, and Apparatus for Monitoring, Regulating, or ControllingFluid Flow (Attorney Docket No. J79WO);

PCT Application No. PCT/US12/71112, filed Dec. 21, 2012 and entitledSystem, Method, and Apparatus for Estimating Liquid Delivery (AttorneyDocket No. J81WO); and

U.S. application Ser. No. 13/723,253, field Dec. 21, 2012 and entitledSystem, Method, and Apparatus for Electronic Patient Care, now U.S.Publication No. US 2013-0191513-A1, published Jul. 25, 2013 (AttorneyDocket No. J85).

BACKGROUND Relevant Field

The present disclosure relates to pumps. More particularly, the presentdisclosure relates to a system, method, and apparatus for liquiddelivery using a syringe pump.

Description of Related Art

Syringe pumps are used in a variety of medical applications, such as forintravenous delivery of liquid medications, for example a patient in anintensive-care unit (ICU), for an extended length of time. Syringe pumpsmay be designed so that needles, tubing, or other attachments areattachable to the syringe pump. Syringe pumps typically include aplunger mounted to a shaft that pushes a liquid out of a reservoir. Thereservoir may be a tube-shaped structure having a port at one end suchthat the plunger can push (i.e., discharge) the liquid out of thesyringe pump. Syringe pumps can be coupled to an actuator thatmechanically drives the plunger to control the delivery of liquid to thepatient.

Syringe pumps may also be used to deliver various drugs includinganalgesics, antiemetics, or other fluids. The medication may beadministered via an intravenous liquid line very quickly (e.g., in abolus) or over a length of time. Syringe pumps may also be used innon-medical applications, such as in microreactors, testing, and/or inchemical processing applications.

SUMMARY

In one aspect of the present disclosure, a pump includes a reservoir, aport, a plunger, and a reference-volume assembly. The reservoir isconfigured to deliver a liquid. The port is coupled to the reservoir andis configured to discharge the liquid. The plunger includes a pistoncoupled to a shaft. The piston is disposed within the reservoir insliding engagement with an inner surface of the reservoir. The pistondefines a liquid side of the reservoir and a non-liquid side of thereservoir whereby movement of the plunger towards the liquid side of thereservoir discharges liquid through the port. The reference-volumeassembly is coupled to the reservoir at an opposite end of the reservoirrelative to the port. The reference-volume assembly includes areference-volume chamber, a speaker, and a reference microphone. Thereference-volume chamber is in acoustic communication with thenon-liquid side of the reservoir. The speaker is disposed within thereference-volume chamber, and the reference microphone is disposedwithin the reference-volume chamber. A variable-volume microphone may bedisposed within the reservoir to sense the sound wave within thereservoir and/or disposed on the reference-volume assembly to sense thesound wave within the reservoir.

In another aspect of the present disclosure, a system may include a pump(as described above), an actuator, a linear position sensor, and aprocessor. The actuator is coupled to the shaft of the pump to actuatethe pump and the linear position sensor is coupled to the shaft to sensea position of the shaft. The processor is coupled to the actuator andthe linear position sensor to estimate a volume of discharged liquid asa function of the position of the shaft.

In another aspect, a system may include a pump (as described above), avariable-volume microphone, and a processor. The variable-volumemicrophone senses the sound wave within the non-liquid side of thereservoir. The processor is operatively coupled to the speaker, and thereference and variable-volume microphones to instruct the speaker togenerate a plurality of acoustic frequencies and estimate a volume ofdischarged liquid as a function of the acoustic feedback from thevariable-volume and reference microphones.

In yet another aspect of the present disclosure, a pump includes areservoir, a port, a plunger, an additional reservoir, an additionalport, an additional plunger, and a reference-volume assembly. Thereservoir is configured to deliver a liquid. The port is coupled to thereservoir and is configured to discharge the liquid. The plungerincludes a piston coupled to a shaft. The piston is disposed within thereservoir in sliding engagement with an inner surface of the reservoir.The piston defines a liquid side of the reservoir and a non-liquid sideof the reservoir whereby movement of the plunger towards the liquid sideof the reservoir discharges liquid through the port.

The additional reservoir is configured to deliver an additional liquid.The additional port is coupled to the additional reservoir and isconfigured to discharge the additional liquid. The additional plungerincludes an additional piston coupled to the additional shaft. Theadditional piston is disposed within the additional reservoir in slidingengagement with an inner surface of the additional reservoir. Theadditional piston defines a liquid side of the additional reservoir anda non-liquid side of the additional reservoir whereby movement of theadditional plunger towards the liquid side of the additional reservoirdischarges liquid through the additional port.

The reference-volume assembly is coupled to the reservoir at an oppositeend of the reservoir relative to the port, and the reference-volumeassembly is further coupled to the additional reservoir at an oppositeend of the additional reservoir relative to the additional port. Thereference-volume assembly includes a reference-volume chamber, aspeaker, and a reference microphone. The reference-volume chamber is inacoustic communication with the non-liquid side of the reservoir, andthe reference-volume chamber is further in acoustic communication withthe non-liquid side of the additional reservoir. The speaker is disposedwithin the reference-volume chamber, and the reference microphonedisposed within the reference-volume chamber. Optionally, one or more ofthe first and second reservoirs are attachable to the reference-volumeassembly.

In another aspect of the present disclosure, the pump includes amanifold. The manifold includes first and second connector ports, adischarge port, and a liquid path. The first connector port is coupledto the port, and the second connector port is coupled to the additionalport. The liquid path fluidly connects together the first and secondconnector ports to the discharge port. The manifold is optionallyattachable to the first and second connector ports.

In another aspect of the present disclosure, the pump includes avariable-volume microphone disposed within the reservoir or on thereference-volume assembly and is configured to sense the sound wavewithin the reservoir. The pump may also include an additionalvariable-volume microphone disposed within the additional reservoir ofon the reference-volume assembly and configured to sense the sound wavewithin the additional reservoir.

In another aspect of the present disclosure, a system for estimatingliquid deliver includes a pump as described above, a variable-volumemicrophone, and a processor. The variable-volume microphone senses thesound wave within the non-liquid side of the reservoir. The processor isoperatively coupled to the speaker, and the reference andvariable-volume microphones. The processor is configured to instruct thespeaker to generate a plurality of acoustic frequencies and to estimatea volume of discharged liquid as a function of the acoustic feedbackfrom the variable-volume and reference microphones.

In yet another aspect of the present disclosure, a pump includes anacoustic housing, a reservoir, a port, a plunger, and a reference-volumeassembly. The reservoir is configured to deliver a liquid and isdisposed within the acoustic housing. The port is coupled to thereservoir and is configured to discharge the liquid. The plunger has apiston coupled to a shaft. The plunger is disposed within the acoustichousing, and the piston is disposed within the reservoir in slidingengagement with an inner surface of the reservoir. The piston defines aliquid side of the reservoir and a non-liquid side of the reservoirwhereby movement of the plunger towards the liquid side of the reservoirdischarges liquid through the port. The reference-volume assembly iscoupled to the acoustic housing through an acoustic port. Thereference-volume assembly includes a reference-volume chamber, aspeaker, and a reference microphone. The reference-volume chamber is inacoustic communication with the acoustic housing via the acoustic port.The speaker is disposed within the reference-volume chamber, and thereference microphone is disposed within the reference-volume chamber.The pump may also include an actuator coupled to the shaft to actuatethe plunger, and the actuator may be disposed within the acoustichousing.

The pump may also include an additional reservoir, an additional port,and an additional plunger. The additional reservoir is configured todeliver an additional liquid, and the additional reservoir is disposedwithin the acoustic housing. The additional port is coupled to theadditional reservoir and is configured to discharge the additionalliquid. The additional plunger has an additional piston coupled to theadditional shaft. The additional plunger is disposed within the acoustichousing, and the additional piston is disposed within the additionalreservoir in sliding engagement with an inner surface of the additionalreservoir. The additional piston defines a liquid side of the additionalreservoir and a non-liquid side of the additional reservoir wherebymovement of the additional plunger towards the liquid side of theadditional reservoir discharges liquid through the additional port.

The pump may also include a manifold. The manifold includes first andsecond connector ports, a discharge port, and a liquid path. The firstconnector port is coupled to the port, and the second connector port iscoupled to the additional port. The liquid path fluidly connectstogether the first and second connector ports to the discharge port. Themanifold is optionally attachable to the first and second connectorports.

In yet an additional aspect of the present disclosure, a system forestimating liquid delivery includes a pump as described above, anactuator, a linear position sensor, and a processor. The actuator iscoupled to the shaft. The linear position sensor is coupled to the shaftand is configured to sense a position of the shaft. The processor isoperatively coupled to the actuator and the linear position sensor toestimate a volume of discharged liquid as a function of the position ofthe shaft, e.g., as determined by the linear position sensor.

In another aspect of the present disclosure, a system for estimatingliquid delivery includes a pump as described above, a variable-volumemicrophone, and a processor. The variable-volume microphone senses thesound wave within the non-liquid side of the reservoir. The processor isoperatively coupled to the speaker, and the reference andvariable-volume microphones. The processor is configured to instruct thespeaker to generate a plurality of acoustic frequencies and estimate avolume of discharged liquid as a function of the acoustic feedback fromthe variable-volume and reference microphones.

In yet another aspect of the present disclosure, a pump includes anacoustic housing, an additional acoustic housing, a reservoir, a port, aplunger, an additional reservoir, an additional port, an additionalplunger, and an a reference-volume assembly. The reservoir is configuredto deliver a liquid and is disposed within the acoustic housing. Theport is coupled to the reservoir and is configured to discharge theliquid. The plunger has a piston coupled to a shaft. The plunger isdisposed within the acoustic housing. The piston is disposed within thereservoir and is in sliding engagement with an inner surface of thereservoir, and the piston defines a liquid side of the reservoir and anon-liquid side of the reservoir whereby movement of the plunger towardsthe liquid side of the reservoir discharges liquid through the port. Theadditional reservoir is configured to deliver an additional liquid. Theadditional reservoir is disposed within the additional acoustic housing.The additional port is coupled to the additional reservoir and isconfigured to discharge the additional liquid. The additional plungerhas an additional piston coupled to the additional shaft. The additionalplunger is disposed within the additional acoustic housing. Theadditional piston is disposed within the additional reservoir in slidingengagement with an inner surface of the additional reservoir. Theadditional piston defines a liquid side of the additional reservoir anda non-liquid side of the additional reservoir whereby movement of theadditional plunger towards the liquid side of the additional reservoirdischarges liquid through the additional port.

The reference volume assembly is coupled to the acoustic housing throughan acoustic port and is coupled to the additional acoustic housingthrough an additional acoustic port. The reference-volume assemblyincludes a reference-volume chamber, a speaker, and a referencemicrophone. The reference-volume chamber is in acoustic communicationwith the acoustic housing via the acoustic port. The reference-volumechamber is in acoustic communication with the additional acoustichousing via the additional acoustic port. The speaker is disposed withinthe reference-volume chamber. The reference microphone is disposedwithin the reference-volume chamber.

The pump may also include an actuator coupled to the shaft to actuatethe plunger. The actuator may be disposed within the acoustic housing.The pump may include an additional actuator coupled to the additionalshaft to actuate the additional plunger.

The pump may also include a manifold. The manifold includes first andsecond connector ports, a discharge port, and a liquid path. The firstconnector port is coupled to the port, and the second connector port iscoupled to the additional port. The liquid path fluidly connectstogether the first and second connector ports to the discharge port. Themanifold is optionally attachable to the first and second connectorports.

In yet an additional aspect of the present disclosure, a system forestimating liquid delivery includes a pump as described above, anactuator, a linear position sensor, and a processor. The actuator iscoupled to the shaft. The linear position sensor is coupled to the shaftand is configured to sense a position of the shaft. The processor isoperatively coupled to the actuator and the linear position sensor andis configured to estimate a volume of discharged liquid as a function ofthe position of the shaft.

In yet another aspect thereof, a system for estimating liquid deliveryincludes the pump as described above, a variable-volume microphone, anda processor. The variable-volume microphone senses the sound wave withinthe non-liquid side of the reservoir. The processor is operativelycoupled to the speaker, and the reference and variable-volumemicrophones. The processor is configured to instruct the speaker togenerate a plurality of acoustic frequencies and estimate a volume ofdischarged liquid as a function of the acoustic feedback from thevariable-volume and reference microphones.

In yet an additional aspect of the present disclosure, a pump includes areservoir, a port, a plunger, and a linear position sensor. Thereservoir is configured to deliver a liquid. The port is coupled to thereservoir and is configured to discharge the liquid. The plunger has apiston coupled to a shaft. The piston is disposed within the reservoirin sliding engagement with an inner surface of the reservoir. The pistondefines a liquid side of the reservoir and a non-liquid side of thereservoir whereby movement of the plunger towards the liquid side of thereservoir discharges liquid through the port. The linear position sensoris configured to sense a position of the shaft.

The pump may also include a housing such that the reservoir is disposedwithin the housing, and the plunger is disposed within the housing. Thepump may also include an actuator coupled to the shaft to actuate theplunger and disposed within the housing. The linear position sensor mayalso be disposed within the housing.

The pump may further comprise an additional reservoir, an additionalport, an additional plunger, and an additional linear position sensor.The additional reservoir is configured to deliver an additional liquid.The additional port is coupled to the additional reservoir and isconfigured to discharge the additional liquid. The additional plungerhas an additional piston coupled to the additional shaft. The additionalpiston is disposed within the additional reservoir in sliding engagementwith an inner surface of the additional reservoir. The additional pistondefines a liquid side of the additional reservoir and a non-liquid sideof the additional reservoir whereby movement of the additional plungertowards the liquid side of the additional reservoir discharges liquidthrough the additional port. The additional linear position sensor isconfigured to sense a position of the additional shaft.

The pump may also include a manifold. The manifold includes first andsecond connector ports, a discharge port, and a liquid path. The firstconnector port is coupled to the port, and the second connector port iscoupled to the additional port. The liquid path fluidly connectstogether the first and second connector ports to the discharge port. Themanifold is optionally attachable to the first and second connectorports.

The pump may also include a housing such that the reservoir and theadditional reservoir are disposed within the housing, and the plungerand the additional plunger are also disposed within the housing.

The pump may also include an actuator coupled to the shaft to actuatethe plunger, and an additional actuator coupled to the additional shaftto actuate the additional plunger. The actuator and the additionalactuator may be disposed within the housing. The linear position sensorand/or the additional linear position sensor may be a capacitive sensorcoupled to the shaft or a linear optical position sensor. The linearposition sensor and/or the additional linear position sensor may bedisposed within the housing.

In some aspects of the present disclosure, the linear position sensorincludes an optical target and an optical ranging assembly. The opticaltarget is coupled to the shaft. The optical ranging assembly isconfigured to determine a range of the optical target thereby estimatinga linear position of the shaft.

The optical target may be a reflective target, and the optical rangingassembly may include an illuminator configured to illuminate thereflective target thereby determining the linear position of the shaftfrom a reflection of the illumination of the reflective target.

The optical target may be a light source, and the optical rangingassembly may be configured to determine the linear position of the shaftfrom a measured intensity of the light source measured by the opticalranging assembly.

In another aspect of the present disclosure, a system for estimatingliquid delivery includes a pump, an actuator, and a processor. Theactuator is coupled to the shaft, and the processor is operativelycoupled to the actuator and the linear position sensor to estimate avolume of discharged liquid as a function of the position of the shaft.

In yet another aspect of the present disclosure, one or more of theherein described pumps may include one or more optional features asdescribed below. One or more of the pistons of a pump as describedherein may comprise a seal disposed along a periphery of the piston. Thereservoir may be cylindrically shaped thereby defining a circular crosssection; the piston can engage an inner surface of the reservoir alongthe circular cross section. The reservoir may be cuboid shaped therebydefining a rectangular cross section, and the piston can engage theinner surface of the reservoir along the rectangular cross section.

The pump may include a vent in fluid communication with the non-liquidside of the reservoir. The vent may be further configured toacoustically seal the non-liquid side of the reservoir from outside thereservoir.

A pump as described herein may include a one-way valve in fluidcommunication with the non-liquid side of the reservoir. The one-wayvalve may be configured to allow gas to enter into the non-liquid sideof the reservoir from outside the reservoir.

One or more of the pumps described herein may include a plunger that ismoveable between a fully discharged position and a fully loaded positionsuch that the reference-volume chamber is in fluid communication withthe non-liquid side of the reservoir when the plunger is positionedanywhere between the fully discharged position and the fully loadedposition.

A pump as described herein may include a reference-volume chamber thatfurther includes a conduit configured to receive the shaft. The shaftmay be in sliding engagement with the conduit. The conduit may furthercomprise a seal configured to receive the shaft and acoustically sealthe non-liquid side of the reservoir as the shaft engages with theconduit. The reference-volume assembly may further comprise an acousticport in acoustic communication with the reference-volume chamber and thenon-liquid side of the reservoir.

A pump as described herein may include a variable-volume microphone. Thenon-liquid side of the reservoir may be configured to receive thevariable-volume microphone for attachment to the inner surface of thereservoir. The variable-volume microphone is configured to sense thesound wave within the non-liquid side of the reservoir. Additionally oralternatively, the variable-volume microphone may be attached to thereference-volume assembly to sense the sound wave within the non-liquidside of the reservoir.

The actuator described herein may be a linear actuator, a screw-typelinear actuator, a linear track actuator, a linear servo, a linearstepper motor, a linear motor, or some other actuator.

In yet an additional aspect of the present disclosure, a method forestimating liquid delivery includes one or more acts, such as: (1)positioning a plunger of a pump in a first position; (2) generating asound wave; (3) applying the sound wave to a reference chamber; (4)communicating the sound wave to a non-liquid side of a reservoir of thepump; (5) sensing the sound wave in the reference chamber; (6) sensingthe sound wave in the non-liquid side of the reservoir of the pump; (7)comparing the sensed sound wave in the reference chamber to the sensedsound wave in the non-liquid side of the reservoir to determine a firstvolume of liquid within the liquid side of the reservoir; (8) actuatingthe plunger of the pump to a second position; (9) comparing the sensedsound wave in the reference chamber to the sensed sound wave in thenon-liquid side of the reservoir to determine a second volume of liquidwithin the liquid side of the reservoir; and/or (10) comparing the firstvolume to the second volume to determine an amount of liquid discharged.

In yet another aspect of the present disclosure, a system for preparinga syringe pump includes a monitoring client, a pharmacy computer, acompounding robot, a syringe pump, and a data download device. Thesyringe pump may be any disclosed above or herein. The monitoring clientis configured to communicate a prescription order via a user interface.The pharmacy computer is in operative communication with the monitoringclient to receive the prescription order. The compounding robot isconfigured to prepare the prescription into at least one liquidcorresponding to the prescription order. The syringe pump is configuredto receive the at least one liquid corresponding to the prescriptionorder. The data download device is configured to download theprescription order into a memory of the pill dispenser. The syringe pumpincludes a reference volume attached thereto. The compounding robot mayfill the syringe pump with the at least one liquid. The compoundingrobot may be in operative communication with the data download device.The compounding robot may instruct the data download device to downloadthe prescription order into the memory of the pill dispenser. The datadownload device may receive the prescription order from the compoundingrobot and/or the pharmacy computer.

BRIEF DESCRIPTION OF THE DRAWINGS

These and other aspects will become more apparent from the followingdetailed description of the various embodiments of the presentdisclosure with reference to the drawings wherein:

FIG. 1 is a illustration of an electronic patient-care system having asyringe pump in accordance with an embodiment of the present disclosure;

FIG. 2 is a block diagram of a system for controlling a syringe pump inaccordance with an embodiment of the present disclosure;

FIG. 3 shows an illustration of a syringe pump having a reference-volumeassembly coupled to the reservoir of the syringe pump for acousticallyestimating the amount of liquid discharged by the syringe pump inaccordance with an embodiment of the present disclosure;

FIG. 4 shows an illustration of a syringe pump having two reservoirs anda reference-volume assembly coupled to the reservoirs for acousticallyestimating the amount of liquid discharged by the syringe pump inaccordance with an embodiment of the present disclosure;

FIG. 5 shows an illustration of a syringe pump having two reservoirsdisposed within an acoustic housing, and a reference-volume assemblycoupled to the acoustic housing for acoustically estimating the amountof liquid discharged by the syringe pump in accordance with anembodiment of the present disclosure;

FIG. 6 shows an illustration of a syringe pump having two reservoirseach disposed within a respective acoustic housing, and areference-volume assembly acoustically coupled to the acoustic housingsfor acoustically estimating the amount of liquid discharged by thesyringe pump in accordance with an embodiment of the present disclosure;

FIG. 7 shows an illustration of a syringe pump having two reservoirs andtwo capacitive sensors each coupled to a respective plunger of arespective reservoir for estimating the amount of liquid discharged bythe syringe pump in accordance with an embodiment of the presentdisclosure;

FIG. 8 shows an illustration of a syringe pump having two reservoirs andtwo reflective targets each coupled to a respective plunger of arespective reservoir for estimating the amount of liquid discharged bythe syringe pump using an optical ranging assembly in accordance with anembodiment of the present disclosure;

FIG. 9 shows an illustration of a syringe pump having two reservoirs andtwo light sources each coupled to a respective plunger of a respectivereservoir for use with an optical ranging assembly for estimating theamount of liquid discharged by the syringe pump in accordance with anembodiment of the present disclosure;

FIG. 10 shows an illustration of a syringe pump having two reservoirsand two linear optical position sensors each coupled to a respectiveplunger of a respective reservoir for estimating the amount of liquiddischarged by the syringe pump in accordance with an embodiment of thepresent disclosure; and

FIGS. 11-12 show a flow chart diagram of a method for estimating liquiddelivery in accordance with an embodiment of the present disclosure.

DETAILED DESCRIPTION

FIG. 1 shows an exemplary arrangement of a system 1 for electronicpatient care in accordance with an embodiment of the present disclosure.The system 1 includes a monitoring client 2 that is linked to a numberof patient-care devices via docks 3 and 11, including an infusion pump 4connected to and delivering from a smaller bag of liquid 5, an infusionpump 6 connected to and delivering from a larger bag of liquid 7, a dripdetection device 8 connected to tubing from the smaller bag 5, and amicroinfusion pump 9. System 1 also includes a syringe pump 10 connectedwirelessly to the monitoring client 2. In some embodiments, themonitoring client 2 may communicate with these patient-care devices in awired fashion, as shown in FIG. 1 for the infusion pumps 4 and 6, andthe microinfusion pump 9 (via docks 3 and 11). Additionally oralternatively, the monitoring client 2 may communicate wirelessly withpatient-care devices, as suggested by the absence of a wired connectionbetween the syringe pump 10 and the monitoring client 2.

In some embodiments, a wired connection between the monitoring client 2and a patient-care device also affords an opportunity for electricalpower to be supplied to the patient-care device from the monitoringclient 2. In this exemplary embodiment, the monitoring client 2 mayinclude the electronic circuitry necessary to convert the voltage topower the patient-care device from either a battery attached to themonitoring client 2 or from an Alternative Current (“AC”) line voltagefed into the monitoring client 2 from a power outlet (not shown) in apatient's room. Additionally or alternatively, the dock 3 supplies powerto the infusion pumps 4 and 6, and to the microinfusion pump 9, e.g.,from a signal generated from an AC line voltage.

In an embodiment, the monitoring client 2 is capable of receivinginformation about each patient-care device with which it is linkedeither directly from the device itself, or via a docking station, suchas, for example, the dock 3 onto which the patient-care device may bemounted. The dock 3 may be configured to receive one or morepatient-care devices via a standardized connection mount, or in somecases via a connection mount individualized for the particular device.For example, infusion pumps 4 and 6 may be mounted to the dock 3 via asimilar connection mount, whereas the microinfusion pump 9, for example,may be mounted to the dock 3 via a connection mount configured for theparticular dimensions of the microinfusion pump's 9 housing.

The dock 3 may be configured to electronically identify the particularpatient-care device being mounted on the docking station, and totransmit this identifying information to the monitoring client 2, eitherwirelessly or via a wired connection. Additionally or alternatively,wireless patient-care devices may transmit the identifying informationwirelessly to the monitoring client 2, e.g., during a discoveryprotocol. Additionally, the particular patient-care device may bepreprogrammed with treatment information (e.g., patient-treatmentparameters such as an infusion rate for a predetermined infusion liquid)that is transmitted to the monitoring client 2. For example, the syringepump 10 may include identity information and treatment information, suchas what medication has been prescribed to the patient, what liquid iswithin the syringe pump's 10 reservoir, how much and how long the liquidis prescribed to be delivered to the patient, who are the authorizedcaregivers, etc. In some embodiments of the present disclosure, themonitoring client 2 communicates with EMR records to verify that thepreprogrammed treatment information is safe for an identified patientand/or the preprogrammed treatment information matches the prescribedtreatment stored in the EMR records.

In some embodiments, the drip detection device 8 may communicate withthe monitoring client 2 either wirelessly or in a wired connection. Ifan aberrant liquid flow condition is detected (e.g., because the tubingto the patient has become occluded), a signal may be transmitted tomonitoring client 2, which (1) may display the flow rate of liquid fromthe liquid container 5 in a user interface either locally on themonitoring client 2, or more remotely to a user interface at a nurse'sstation or a handheld communications device, (2) may trigger an auditoryor visual alarm, and/or (3) may cause the monitoring client 2 to alterthe rate of infusion of a pump 4 connected to a bag 5, by eitherterminating the infusion or otherwise changing the pumping rate Theaberrant liquid flow condition may also cause an audible alarm (and/orvibration alarm) on the infusion pump 4 or the drip detection device 8,or cause the infusion pump 4 to modify or stop the pumping, e.g., whenthe aberrant liquid flow condition exceed predefined ranges ofoperation.

The alarms may occur simultaneously on several devices or may follow apredetermined schedule. For example, when an occlusion occurs in a lineconnected to the infusion pump 4, (1) the drip detection device 8 alarmsusing its internal speaker and an internal vibration motor, (2)thereafter, the infusion pump 4 alarms using its internal speaker and aninternal vibration motor, (3) next, the monitoring client 2 alarms usingits internal speaker and an internal vibration motor, and (4) finally, aremote communicator (e.g., a smart phone, blackberry-based phone,Android-based phone, iphone, etc.) alarms using its internal speaker andan internal vibration motor. In some embodiments, the syringe pump 10may be connected to the drip detection device 8 and detect aberrantliquid flow conditions as described above.

In some embodiments, the syringe pump 10 may be programmable to allowfor continued operation at a predetermined pumping rate shouldcommunications fail between the monitoring client 2 and the syringe pump10, either because of a malfunction in the monitoring client 2, in thecommunications channel between the monitoring client 2 and the syringepump 10, or in the syringe pump 10 itself. In some embodiments, thisindependent function option is enabled when the medication being infusedis pre-designated for not being suspended or held in the event of amalfunction in other parts of the system. In some embodiments, thesyringe pump 10 is programmed to operate independently in a fail safemode and may also be configured to receive information from a dripdetection device 8 directly, rather than through a monitoring client 2(e.g., in embodiment where the drip detection device 8 is used inconjunction with the syringe pump 10); with this option, the syringepump 10 may be programmed, in some embodiments, to stop an infusion ifthe drip detection device 8 detects an aberrant flow condition (such as,e.g., a free-flow condition or an air bubble present in the infusionline). In some embodiments, one or more of the pumps 4, 6, and 10 mayhave internal liquid flow meters and/or can operate independently as astand-alone device. Additionally or alternatively, an internal liquidflow meter of the syringe pump 10 may be independently determined by aflow meter of the drip detection device 8 by the monitoring client 2, inembodiments where the devices 8 and 10 are used together.

The monitoring client 2 may also remotely send a prescription to apharmacy. The prescription may be a prescription for infusing a fluidusing the syringe pump 10. The pharmacy may include one or morecomputers connected to a network, e.g., the internet, to receive theprescription and queue the prescription within the one or morecomputers. The pharmacy may use the prescription to compound the drug(e.g., using an automated compounding device coupled to the one or morecomputers or manually by a pharmacists viewing the queue of the one ormore computers), pre-fill a fluid reservoir or cartridge of a syringepump 10, and/or program the syringe pump 10 (e.g., a treatment regime isprogrammed into the syringe pump 10) at the pharmacy in accordance withthe prescription. The reservoir or cartridge may be automatically filledby the automated compounding device and/or the syringe pump 10 may beautomatically programmed by the automated compounding device. Theautomated compounding device may generate a barcode, RFID tag and/ordata. The information within the barcode, RFID tag, and/or data mayinclude the treatment regime, prescription, and/or patient information.The automated compounding device may: attach the barcode to the syringepump 10 or to the reservoir, cartridge, or disposable portion of thesyringe pump 10; attach the RFID tag to the syringe pump 10 or thereservoir, cartridge, or disposable portion of the syringe pump 10;and/or program the RFID tag or memory within the syringe pump 10 or thereservoir, cartridge, or disposable portion of the syringe pump 10 withthe information or data. The data or information may be sent to adatabase that associates the prescription with the syringe pump 10 orthe reservoir, cartridge, or disposable portion of the syringe pump 10,e.g., using a serial number or other identifying information within thebarcode, RFID tag, or memory.

The syringe pump 10 may have a scanner, e.g., an RFID interrogator thatinterrogates a reservoir, disposable portion, or cartridge of thesyringe pump 10 to determine that it is the correct fluid within thefluid reservoir or it is the correct fluid reservoir, disposable portionor cartridge, the treatment programmed into the syringe pump 10corresponds to the fluid within the fluid reservoir, disposable portionor cartridge, and/or the syringe pump 10 and reservoir, disposableportion or cartridge of the syringe pump 10 are correct for theparticular patient (e.g., as determined from a patient's barcode, RFID,or other patient identification). For example, a serial number of areservoir, disposable portion as scanned by the syringe pump 10 iscompared to a serial number in electronic medical records to determineif it correctly corresponds to a patient's serial number within theelectronic medical records; the syringe pump 10 may scan a RFID tag orbarcode of a patient to obtain a serial number of a patient which isalso compared to the patient's serial number within the electronicmedical records (e.g., the serial number of a reservoir, disposableportion, or cartridge of the syringe pump 10 or a serial number storedwithin memory of the syringe pump 10 should be associated with thepatient's serial number as scanned within the electronic medicalrecords). The syringe pump 10 may issue an error or alarm if the serialnumbers do not match, in some specific embodiments. Additionally oralternatively, the monitoring client 6 may scan the reservoir,disposable portion, cartridge, or syringe pump 10 to determine that itis the correct fluid within the fluid reservoir, it is the correct fluidreservoir, the treatment programmed into the syringe pump 10 correspondsto the fluid within the fluid reservoir or cartridge, and/or the fluidreservoir and syringe pump 10 are correct for the particular patient(e.g., as determined from a patient's barcode, RFID, or other patientidentification). Additionally or alternatively, the monitoring client 6or syringe pump 10 may interrogate an electronic medical recordsdatabase and/or the pharmacy to verify the prescription or download theprescription, e.g., using a barcode serial number on the syringe pump10, or a reservoir, cartridge, or disposable portion of the syringe pump10.

The liquid being delivered to a patient may be monitored by themonitoring client 2 to determine if all the medications being deliveredare safe for the patient. For example, the monitoring client 2 may logthe medication delivered from the syringe pump 10 as communicated by thesyringe pump 10 to the monitoring client 2, and the monitoring client 2may also log the medication being delivered by the infusion pumps 4 and6, and/or the microinfusion pump 9. The monitoring client 1 may make adetermination from the logged data to determine if the aggregate amountsand types of medication being delivered are safe. For example, themonitoring client 2 may determine if the IV bag 5 is contraindicatedwith the medication in the syringe pump 10. Additionally oralternatively, in some embodiments, the monitoring client 2 may monitorthe delivery of the liquid in the IV bag 8 and one or more bolusesdelivered by the syringe pump 10 to determine if the total dose exceedsa predetermined threshold, e.g., the medication in the IV bag 5 andsyringe pump 10 may be the same type or class of drug, and themonitoring client 2 may determine if the drugs are safe when combined asdelivered to the patient. The syringe pump 10 may also communicate withthe infusion pumps 4 and 6, and/or the microinfusion pump 9 to make thesame determination; In this exemplary embodiment, the syringe pump 10may communicate with the devices directly (via wirelessly or wiredcommunications) or through the monitoring client 2 (via wirelessly orwired communications). In some embodiments of the present disclosures,one or more communication modules (e.g., each having the capabilities tocommunicate via one or more protocols) may be connected to the syringepump 10 and/or may be connected together and then connected to thesyringe pump 10 to enable the syringe pump 10 to communicate via thecommunication modules.

The syringe pump 10 includes a touch screen interface 11 (which may bedetachable), a start button 12, and a stop button 13. The user interface11 may be used to program treatment regimes, such as flow rates, bolusamounts, or other treatment parameters. After a treatment regime isprogrammed into the syringe pump 10, the syringe pump 10 may query adatabase (e.g., Electronic Medical Records (“EMR”), Drug Error ReductionSystem (“DERS”), or other database) to determine if the treatment regimeis safe for the particular patient or for any patient. For example, thesyringe pump 10 may query the EMR database (e.g., via a wireless link,wired link, WiFi, cell-phone network, or other communicationstechnology) to determine if the treatment regime from the syringe pump10 is safe based upon patient information stored (e.g., age, weight,allergies, condition, etc.) in the EMR records. Additionally oralternatively, the syringe pump 10 may query the DERS database (e.g.,via a wireless link, wired link, WiFi, cell-phone network, or othercommunications technology) to determine if the treatment regime from thesyringe pump 10 is safe based upon predetermined safety criteria in theDERS records

In some embodiments, if the treatment regime is determined to be safe, aprompt may request user confirmation of the treatment regime. After userconfirmation, the user (e.g., caregiver, nurse, or other authorizedperson) may press the start button 12. In some embodiments, the stopbutton 13 may be pressed at any time to stop treatment.

In some embodiments, if the EMR and/or DERS determines that thetreatment regime exceeds a first set of criteria, treatment may continueif the user confirms the treatment (e.g., with an additional warning,user pass code, and/or additional authentication or authorization,etc.); in this embodiment, the EMR or DERS may prevent the treatmentfrom being delivered if the EMR and/or DERS determines that thetreatment regime exceeds a second set of criteria, e.g., the treatmentis not safe under any circumstances for any patient, for example.

FIG. 2 is a block diagram of a system 14 for controlling a syringe pumpin accordance with an embodiment of the present disclosure. The system14 of FIG. 2 may be used to control the syringe pump 10 of FIG. 1, orthe syringe pumps of FIGS. 3-10 described below.

The system 14 includes one or more sensors 15, a control system 16,driver circuitry 17, and an actuator 18. The system 14 operates tocontrol a position of a plunger within a syringe pump using the actuator18. The processor 21 may control the actuator 18 to actuate any plungerdescribed herein. For example, the actuator 18 may be coupled to theshaft 19 of FIG. 3 (described below) to control the position of theplunger 20.

The control system 16 includes a processor 21 coupled to a memory 22.The processor 21 and memory 22 may be coupled together through a serialconnection, a parallel connection, a memory bus, or other datacommunications link. The processor 21 may include one or more cores, mayuse any instruction set, and/or may use any instruction set architectureor microarchitecture. For example, the processor 21 may have the VonNeumann architecture, the Harvard architecture, may be amicrocontroller, may use a MIPS instruction set, a RISC instruction set,and/or a CISC instruction set, etc.

The control system 16 includes a therapy layer 23 and a control layer24. The therapy layer 23 may instruct the control layer 24 when and howmuch liquid to discharge from a syringe pump 10. For example, thetherapy layer 23 may instruct the control layer 24 to discharge 10millimeters of liquid per minutes, etc. The therapy layer 23 may alsocontrol the stop time and start time of liquid delivery to the patient.For example, the therapy layer 23 may include a liquid deliver rateprofile based upon time. The therapy layer 23 may command a liquiddischarge rate to the control layer 24 as the values within the liquiddeliver rate profile indicate that it is time to change the deliveryrate. The control layer 24 receives a target liquid discharge rate fromthe therapy layer 23 and uses the target liquid discharge rate as a setpoint in a control loop and controls the position of the actuator 18 toachieve the set point. For example, the control layer 24 may implement aproportional-integral-derivative (“PID”) control algorithm having anoutput to the driver circuitry 17 and feedback from the one or moresensor 15, such as the piston position sensor 25 and/or a volume sensor26. The control layer 24, in various embodiments, may have a targetdischarge rate, a target volume to discharge, a target remaining liquidvolume, some combination thereof, or the like.

The therapy layer 23 and control layer 24 may be implemented inhardware, software, software in execution on the processor 21, firmware,microcode, assembly, virtualization, bytecode, VHDL, Verilog, in a PAL,in a PLD, in a CPLD, the like, or some combination thereof. For example,the therapy layer 23 and/or the control layer 24 may be stored in thememory 22 as an operative set of processor 21 executable instructionsconfigured for execution on one or more of the processors 21. The memory22 may be volatile memory, non-volatile memory, a hard disk, magneticstorage, flash storage, EEPROM, ROM, optical-memory, othernon-transitory processor readable medium, the like, or some combinationthereof.

The control system 16 outputs one or more signals to the driver circuit17 that drives the actuator 18. The driver circuitry 17 may includepower MOSFETS, voltage converters, power converters, and/or additionalcircuitry to receive instructions from the control system 16 and applyone or more sufficient signals to the actuator 18. As the actuator 18actuates, the sensors 15 are used by the control system 16 as feedback,including the piston position sensor 25 and/or the volume sensor 26. Thepiston position sensor 25 may be a linear position sensor and may beused with any position sensor described herein. The volume sensor 26 maybe, in some embodiments, an acoustic volume sensing (“AVS”) sensor andis used with a speaker, a reference microphone, and a variable-volumemicrophone (of any sufficient syringe pump described herein) to estimatethe amount of liquid discharged or contained within a reservoir. In someembodiments, one of the sensors 25 and 26 is used, both are used, and/ornone are used.

FIG. 3 shows an illustration of a syringe pump 27 having areference-volume assembly 28 coupled to the reservoir 29 of the syringepump 27 for acoustically estimating the amount of liquid discharged bythe syringe pump 27 in accordance with an embodiment of the presentdisclosure. The syringe pump 27 may use acoustic volume sensing (“AVS”)to estimate the volume of liquid within the liquid side 31 of thereservoir 29 and/or to estimate the liquid discharged from the liquidside 32 of the reservoir 29 using a speaker 6, a reference microphone37, and a variable-volume microphone 38.

The syringe pump includes a reservoir 29 and a plunger 20. The plungerincludes a shaft 19 and a piston 30 in sliding engagement with the innersurface of the reservoir 29. The shaft 19 passes through thereference-volume assembly 28 through a seal 41. The piston 30 defines aliquid side 31 and a non-liquid side 32. As the piston 30 moves towardsa port 33, the liquid is discharged through the port 33. The piston 30may include one of more seals 34 disposed along a periphery of thepiston 30 to provide a sufficient fluid seal between the liquid side 31and the non-liquid side 32 of the reservoir 29. The port 33 may becoupled to a needle, tube, manifold, and/or may include a connector,such as screw-type threads formed thereon.

The reference volume assembly 28 includes a reference volume 35. Thereference volume 35 may have a small laser drilled hole to the ambientair to allow air to fill the reference volume 35 as the piston 30 moves.The reference volume assembly 28 also includes a speaker 36, a referencemicrophone 37, and a variable volume microphone 38. The speaker 36generates the sound wave that is applied to the reference volume 35. Theterm “sound wave” may include waves at a human perceptible frequency, afrequency not perceptible by a human, a frequency not perceptible by aliving organism, ultrasonic frequencies, acoustic frequencies, or otherfrequency of mechanical vibration. The sound wave travels through anacoustic port 39 into the variable volume 40. The reference microphone37 senses the sound wave within the reference volume 35 and thevariable-volume microphone 38 senses the sound wave within the variablevolume 40. A processor, e.g., the processor 21 of FIG. 2, is inoperative communication with the speaker 36, and the reference andvariable volume microphones 37 and 38. The processor 21 instructs thespeaker 36 to generate a plurality of acoustic frequencies and measuresthe magnitude and/or phase of the sound wave sensed by the referencemicrophone 37 and the variable-volume microphone 38. The acousticresponse can be correlated with the volume of the variable volume 40,e.g., the resonance frequency may be correlated with the volume of thevariable volume 40. The processor may subtract: (1) the volume of thevariable volume 40 (as measured from the acoustic response), (2) thevolume displaced by the piston 30, and (3) the volume of the shaftlocated within the reservoir 29 from the predetermined total volume ofthe reservoir 29 to estimate the volume of the liquid 31 remaining inthe liquid side 31 of the reservoir 29.

The processor 21 may use the speaker 36, the reference microphone 37,and the variable-volume microphone 38 to estimate the volume of fluidduring a first sweep. The processor 21 may then move the shaft 19 (viaactuation by an actuator) and make a second sweep. The processor 21 maycompare the two volumes to determine the amount of liquid dischargedthrough the port 33 during the actuation of the actuator coupled to theshaft 19.

FIG. 4 shows an illustration of a syringe pump 42 having two reservoirs43 and 44, and a reference-volume assembly 45 coupled to the reservoirs43 and 44 for acoustically estimating the amount of liquid discharged bythe syringe pump 42 in accordance with an embodiment of the presentdisclosure. The syringe pump 42 may use acoustic volume sensing (“AVS”)to estimate the volume of liquid within a liquid side 55 of a reservoir43, the volume of liquid within a liquid side 56 of a reservoir 44, thevolume of liquid discharged from the liquid side 55 of the reservoir 43,and/or the volume of liquid discharged from the liquid side 56 of thereservoir 44 using a speaker 51, a reference microphone 52, avariable-volume microphone 54, and a variable-volume microphone 53.

The syringe pump 42 includes reservoirs 43 and 44, which may beattachable and/or removable from the syringe pump 42. For example, thereservoirs 43 and 44 may be preloaded and snap into the housing 69 suchthat the reservoirs 43 and 44 snap into the reference-volume assembly45. In some embodiments, the syringe pump 42 optionally includes ahousing 69 and a cap 70. The housing 69 may be attachable to the cap 70,and/or the housing 69 may be attachable to other caps.

The syringe pump 42 includes a reference-volume assembly 45 having areference-volume chamber 46 that is acoustically coupled to thenon-liquid sides 47 and 48 of the two reservoirs 43 and 44,respectively. The reference-volume chamber 46 is coupled to thenon-liquid side 47 of the reservoir 43 via an acoustic port 49, and thereference-volume chamber 46 is coupled to the non-liquid side 48 of thereservoir 44 via the port 50.

The reference-volume chamber 46 includes a speaker 51 and a referencemicrophone 52, which are both coupled to the processor 21 of FIG. 2. Thereference-volume assembly 45 also includes a variable-volume microphone53 configured to sense the sound wave within the non-liquid side 48 ofthe reservoir 44, and another variable volume microphone 54 configuredto sense the sound wave in the non-liquid side 47 of the reservoir 43.The two variable-volume microphones 53 and 54 are coupled to theprocessor 21 of FIG. 2. The processor 21 may account for the volume ofthe shafts 57 and 58, and the volume of the pistons 59 and 60.

The syringe pump 42 also includes a manifold 61 that connects the ports62 and 63 of the reservoirs 43 and 44, respectively, and provides aliquid path to a discharge port 64. The manifold 61 may be attachableand/or disposable. The discharge port 64 may be connected to a needle65, a tube (not shown), a fitting (not shown), and/or may include anyknown connector or port. The needle 65 may be attachable and/ordisposable.

The processor 21 of FIG. 2 uses the speaker 51 to generate a pluralityof acoustic frequencies that are received by the reference microphone52, and the variable-volume microphones 53 and 54. The processor 21 usesthe acoustic responses of the non-liquid sides 47 and 48 to estimatetheir respective volumes. The two values are used by the processor 21 toestimate the volume of the liquid sides 55 and 56 of the two reservoirs43 and 44.

FIG. 5 shows an illustration of a syringe pump 66 having two reservoirs67 and 68 disposed within an acoustic housing 71, and a reference-volumeassembly 29 coupled to the acoustic housing 71 for acousticallyestimating the amount of liquid discharged by the syringe pump 66 inaccordance with an embodiment of the present disclosure. The syringepump 66 may use acoustic volume sensing (“AVS”) to estimate the volumeof liquid within a reservoir 67, the volume of liquid within a reservoir68, the volume of liquid discharged from the reservoir 67, and/or thevolume of liquid discharged from the reservoir 68 using a speaker 36, areference microphone 37, and a variable-volume microphone 81. Theacoustic housing 71 may be attachable and/or disposable. For example,the acoustic housing 71 may snap fit into the housing 88. The housing 88may be reusable and/or disposable. A manifold 61 and/or needle 109 maybe attachable and/or disposable. A protection screen 72 prevents debrisfrom entering into and/or affecting the acoustic port 39.

The syringe pump 66 includes reservoirs 67 and 68 disposed within theacoustic housing 71. The reservoir 67 has a piston 75 of a plunger 73disposed therein. The reservoir 76 has a piston 76 of a plunger 74disposed therein. The reservoir 67 has a stop 145 attached at an endthereof that prevents the piston 75 from moving out of the reservoir 67.Additionally, the reservoir 68 has a stop 146 attached at an end thereofthat prevents the piston 76 from moving out of the reservoir 68.

The plunger 73 includes a shaft 77, and the plunger 74 includes a shaft78 that are wholly disposed within the acoustic housing 71.Additionally, an actuator 79 is coupled to the shaft 77 to actuate theshaft 77, and another actuator 80 is coupled to the shaft 78 to actuatethe shaft. Both of the actuators 79 and 80, and the two shafts 77 and 78are disposed within the acoustic housing 71 in the embodiment shown inFIG. 5. Because the shafts 77 and 78, and the actuators 79 and 80 aredisposed within the acoustic housing 71, movement of the shafts 77 and78 and the actuators 79 and 80 (as liquid is discharged) does not affectthe volume as sensed by the processor 21 of FIG. 2 (via the variablevolume microphone 81 disposed within the acoustic housing 71);therefore, in the embodiment shown in the FIG. 5, the processor 21 ofFIG. 2 does not have to compensate for varying volume caused by themovement of a shafts 77 and 78 and/or the actuators 79 and 80.

FIG. 6 shows an illustration of a syringe pump 82 having two reservoirs83 and 84 each disposed within a respective acoustic housing (85 and86), and a reference-volume assembly 87 acoustically coupled to theacoustic housings 85 and 86 for acoustically estimating the amount ofliquid discharged by the syringe pump 82 in accordance with anembodiment of the present disclosure. The syringe pump 82 may useacoustic volume sensing (“AVS”) to estimate the volume of liquid withina reservoir 83, the volume of liquid within a reservoir 84, the volumeof liquid discharged from the reservoir 83, and/or the volume of liquiddischarged from the reservoir 84 using a speaker 36, a referencemicrophone 37, a variable-volume microphone 53, and a variable-volumemicrophone 54. The acoustic housings 85 and 86 may be removable,attachable, permanently fixed to the housing 89, and/or snap-fit intothe housing 89. Additionally or alternatively, the reservoirs 83 and 84may be removable, attachable, disposable, and/or may snap-fit into thehousing 89. The manifold 61 and the needle 109 may be attachable and/orremovable. The syringe pump includes 82 includes an actuator 90 coupledto a shaft 91 to actuate the shaft 91. The actuator 90 and the shaft 91of the plunger 93 are disposed within the acoustic housing 85 therebythe processor 21 of FIG. 2 does not have to account for the movement ofthe shaft 91 and/or the actuator 90. The syringe pump includes 82 alsoincludes an actuator 92 coupled to a shaft 94 to actuate the shaft 94.Likewise, the actuator 92 and the shaft 94 of the plunger 95 aredisposed within the acoustic housing 86 thereby the processor 21 of FIG.2 does not have to account for the movement of the shaft 94 and theactuator 92. The reference-volume assembly 87 is coupled to the acoustichousing 85 via an acoustic port 96 and to the acoustic housing 86 viaanother acoustic port 97

FIG. 7 shows an illustration of a syringe pump 98 having two reservoirs99 and 100 and two capacitive sensors 101 and 102 each coupled to arespective plunger 103 and 104 of a respective reservoir (99 and 199,respectively) for estimating the amount of liquid discharged by thesyringe pump 98 in accordance with an embodiment of the presentdisclosure. The syringe pump 98 includes an actuator 90 coupled to theshaft of the plunger 103 to actuate the plunger 103. And, the syringepump 98 also includes an actuator 92 coupled to the shaft of the plunger104 to actuate the plunger 103.

The processor 21 of FIG. 2 may be coupled to the capacitive sensors 101and 102 to determine the linear position of the plungers 103 and 104,and to estimate the volume that remains in the reservoirs 99 and 100.For example, the processor 21 may model the reservoir as a cylinder andmay know how the feedback from the capacitors sensors 101 and 102correspond to the position of the pistons 105 and 106 of the plungers103 and 104, respectively. That is, the position of the pistons 105 and106 may be used to estimate the volume of liquid in each of thereservoirs 99 and 100 by modeling the liquid side of the pistons 105 and106 as cylinders.

The syringe pump 98 also includes a housing 107 that maybe be removableand/or disposable from the non-disposable housing 108. Additionally oralternatively, the syringe pump 98 also includes a manifold 153 that maybe removable and/or disposable from the non-disposable housing 108. Thesyringe pump 98 may also optionally include a needle 109 that is coupledto the manifold 108. The needle 109 may be removable and/or disposable.

FIG. 8 shows an illustration of a syringe pump 110 having two reservoirs111 and 112 and two optical targets 113 and 114 each coupled to arespective plunger 118 or 119 of a respective reservoir (111 and 112,respectively) for estimating the amount of liquid discharged by thesyringe pump 110 using an optical ranging assembly 115 in accordancewith an embodiment of the present disclosure. The syringe pump 110includes a housing 154 that may be attachable and/or removable (e.g.,disposable) from an outer housing 155. Additionally or alternatively,the reservoirs 111 and 112 may be attachable and/or removable from thehousing 154 (and may be disposable). The manifold 153 and/or the needle109 may be attachable, removable, and/or disposable.

The syringe pump 110 includes an actuator 90 coupled to the shaft of theplunger 118 to actuate the plunger 118. And, the syringe pump 110 alsoincludes an actuator 92 coupled to the shaft of the plunger 119 toactuate the plunger 119.

The processor 21 of FIG. 2 may estimate the amount of liquid in thereservoirs 111 and 112 similarly to the way as shown in the embodimentof FIG. 7. The optical ranging assembly includes twoilluminators/sensors 116 and 117. The illuminator/sensor 116 shines alight on the optical target 113, which is reflected back to theilluminator/sensor 116. The optical ranging assembly 115 may use time offlight and/or intensity to estimate the position of the plunger 118.Likewise, the illuminator/sensor 117 shines a light on the opticaltarget 114, which is reflected back to the illuminator/sensor 117. Theoptical ranging assembly 115 may use time of flight and/or intensity asreceived to estimate the position of the plunger 119.

The light from the illuminators/sensors 116 and 117 may be from an LED,laser, may be infrared, visible or invisible light, and may bemodulated, e.g. to save power, etc.

FIG. 9 shows an illustration of a syringe pump 120 having two reservoirs121 and 122 and two light sources 123 and 124 each coupled to arespective plunger 126 and 127 of a respective reservoir (121 and 122,respectively) for use with an optical ranging assembly 125 forestimating the amount of liquid discharged by the syringe pump inaccordance with an embodiment of the present disclosure. The syringepump 120 includes a housing 156 that may be attachable and/or removable(e.g., disposable) from an outer housing 157. Additionally oralternatively, the reservoirs 121 and 122 may be attachable and/orremovable from the housing 156 (and may be disposable). The manifold 153and/or the needle 109 may be attachable, removable, and/or disposable.The syringe pump 120 includes an actuator 90 coupled to the shaft of theplunger 126 to actuate the plunger 126. And, the syringe pump 120 alsoincludes an actuator 92 coupled to the shaft of the plunger 127 toactuate the plunger 127.

The optical ranging assembly 126 includes sensors 128 and 160. Thesensors 128 and 160 measure the intensity of the light sources 123 and124 (e.g., LEDs) and correlates the measured intensity with a positionof the plungers 126 and 127. The processor 21 may modulate the lightsources 123 and 124 such that only one of the light sources 123 and 124is active during a measurement of a respective sensors 128 and 160. Insome embodiments, one of the light sources 123 and 124 may be activewhile both of the sensors 128 and 160 are used to estimate a position ofa respective plunger (of plungers 126 and 127).

FIG. 10 shows an illustration of a syringe pump 129 having tworeservoirs 130 and 131 and two linear optical position sensors 132 and133 each coupled to a respective plunger (i.e., 134 and 135respectively) of a respective reservoir (i.e., 130 and 131,respectively) for estimating the amount of liquid discharged by thesyringe pump 129 in accordance with an embodiment of the presentdisclosure.

The syringe pump 129 includes a housing 158 that may be attachableand/or removable (e.g., disposable) from an outer housing 159.Additionally or alternatively, the reservoirs 130 and 131 may beattachable and/or removable from the housing 158 (and may bedisposable). The manifold 153 and/or the needle 109 may be attachable,removable, and/or disposable.

The linear optical position sensors 132 and 133 may be a linear opticalencoder. The processor 21 of FIG. 2 uses the feedback from the linearoptical position sensors 132 and 133 to estimate the volume of liquidwithin the respective reservoirs 130 and 131, e.g., by cylinder volumeapproximation, or other geometry approximation.

FIGS. 11-12 show a flow chart diagram of a method 136 for estimatingliquid delivery in accordance with an embodiment of the presentdisclosure. The method 136 may be used with any pump disclosed herein,e.g., the syringe pump 10 of FIG. 1, the syringe pump 27 of FIG. 3, thesyringe pump 42 of FIG. 4, the syringe pump 66 of FIG. 5, the syringepump 82 of FIG. 6, the syringe pump 98 of FIG. 7, the syringe pump 110of FIG. 8, the syringe pump 120 of FIG. 9, and/or the syringe pump 129of FIG. 10.

Act 137 positions a plunger of a pump in a first position. Act 138generates the sound wave. Act 139 applies the sound wave to a referencechamber. Act 140 communicates the sound wave to a non-liquid side of areservoir of the pump. Act 141 senses the sound wave in the referencechamber. Act 142 senses the sound wave in the non-liquid side of thereservoir of the pump. Act 143 compares the sensed sound wave in thereference chamber to the sensed sound wave in the non-liquid side of thereservoir to determine a first volume of liquid within the liquid sideof the reservoir. Act 144 actuates the plunger of the pump to a secondposition. Act 147 applies the sound wave to the reference chamber. Act148 applies the sound wave to the non-liquid side of a reservoir of thepump. Act 149 senses the sound wave in the reference chamber. Act 150senses the sound wave in the non-liquid side of the reservoir of thepump. Act 151 compares the sensed sound wave in the reference chamber tothe sensed sound wave in the non-liquid side of the reservoir todetermine a second volume of liquid within the liquid side of thereservoir. Act 152 compares the first volume to the second volume todetermine an amount of liquid discharged.

Acoustic Volume Sensing

The follow discussion describes acoustic volume sensing that may beperformed by the processor 21 of FIG. 2 with a speaker and twomicrophones (e.g., a reference microphone and a variable-volumemicrophone) of a syringe pump, e.g., syringe pump 27 of FIG. 3, syringepump 42 of FIG. 3, syringe pump 66 of FIG. 5, and/or syringe pump 82 ofFIG. 6; AVS may be used to estimate liquid within a reservoir disclosedherein, to estimate an amount of liquid discharged from a reservoirdisclosed herein, and/or to estimate a liquid discharge rate of areservoir disclosed herein. Table 1 shows the definition of variousterms as follows:

TABLE 1 Term Definition Symbols P Pressure p Pressure Perturbation VVolume v Volume Perturbation γ Specific Heat Ratio R Specific GasConstant ρ Density Z Impedance f Flow friction A Cross sectional Area LLength ω Frequency ζ Damping ratio α Volume Ratio Subscripts 0 SpeakerVolume 1 Reference Volume 2 Variable Volume k Speaker r Resonant Port zZero p Pole

-   -   The acoustic volume sensor (“AVS”) measures the fluid volume        displaced by the non-liquid side of a reservoir in the AVS        chamber, e.g., an acoustic housing or within a reservoir, etc.        The sensor does not directly measure the fluid volume, but        instead measures the variable volume of air, V2, within the AVS        chamber; if the total volume of AVS chamber remains constant,        the change in the V2 will be the direct opposite of the change        in the fluid volume. The AVS chamber is the volume of air in        fluid communication with a variable-volume microphone beyond the        acoustic port. For example, in FIG. 3, the non-liquid side 32 of        the reservoir 29 is the variable volume and the reference volume        35 is V1.

The volume of air, V2, is measured using an acoustic resonance. Atime-varying pressure is established in the fixed volume of thereference chamber, V1, using a speaker. This pressure perturbationcauses cyclic airflow in the acoustic port connecting the two volumes,which in turn causes a pressure perturbation in the variable volume. Thesystem dynamics are similar to those of a Helmholtz oscillator; the twovolumes act together as a “spring” and the air in the port connectingthe volumes as a resonant mass. The natural frequency of this resonanceis a function of the port geometry, the speed of sound, and the variablevolume. The port geometry is fixed and the speed of sound can be foundby measuring the temperature; therefore, given these two parameters, thevariable volume can be found from the natural frequency. In someembodiments of the present disclosure, a temperature sensor is usedwithin the acoustic housing and/or within the non-liquid side of areservoir. In some embodiments, the temperature is considered to be apredetermined fixed value, e.g., is assumed to be room temperature, etc.

The natural frequency of the system is estimated by measuring therelative response of the pressures in the two volumes to differentfrequency perturbations created by the speaker. A typical AVSmeasurement will consist of taking an initial measurement. The liquid isthen released from the liquid side of one or more reservoirs anddelivered to the patient (after which a second volume measurement istaken). The difference between these measurements will be the volume ofliquid delivered to the patient. In some embodiments a measurement willbe taken before filling the liquid side of the one or more reservoirsand/or prior to discharging the liquid, e.g., when the syringe pump ispreloaded, to detect any failures of the fluidic system.

An AVS measurement may occur in accordance with the following acts: (1)the processor 21 will turn on power to the AVS electronics, enable theADC of the processor 21 of FIG. 2, and initialize an AVS algorithm; (2)an AVS measurement consists of collecting data at a number of differentfrequencies; (3) optionally measuring the temperature; and (4) thenrunning an estimation routine based on the collected data to estimatethe volume of liquid in the liquid side of a reservoir.

To collect data at each frequency, the speaker is driven sinusoidally atthe target frequency and measurements are taken from the two microphonesover an integer number of wavelengths, e.g., the reference microphoneand the variable volume microphone (as described above). Once the datahas been collected, the processor 21 of FIG. 1 performs a discreteFourier transform algorithm on the data to turn the time-series datafrom the microphones into a single complex amplitude. Integrity checksare run on the data from the microphones to determine if the data isvalid, e.g., the response is within a predetermined phase and/oramplitude range of the acoustic frequency.

The frequency measurements are taken at a number of differentfrequencies. This sine-sweep is then used by the estimation routine toestimate the variable volume. After the estimation is complete, otherintegrity checks is may be performed on the whole sine sweep, includinga secondary check by the processor 21 of FIG. 2.

In some embodiments, after the processor 21 of FIG. 2 verifies themeasurement integrity, the volume estimates are finalized and the sensoris powered off.

AVS Resonance Model

The governing equations for the AVS system can be found fromfirst-principles given a few simplifying assumptions. The system ismodeled as two linearized acoustic volumes connected by an idealizedacoustic port.

Modeling the Acoustic Volumes

The pressure and volume of an ideal adiabatic gas can be related byEquation 1 as follows:

PV ^(γ) =K  (1),

where K is a constant defined by the initial conditions of the system.Equation 1 can be written in terms of a mean pressure, P, and volume, V,and a small time-dependent perturbation on top of those pressures, p(t),v(t) as illustrated in Equation 2 as follows:

(P+p(t))(V+v(t))^(γ) =K  (2).

Differentiating Equation 2 results in Equation 3 as follows:

{dot over (p)}(t)(V+v(t))^(γ)+γ(V+v(t))^(γ−1)(P+p(t)){dot over(v)}(t)=0  (3)

Equation 3 simplifies to Equation 4 as follows:

$\begin{matrix}{{{\overset{.}{p}(t)} + {\gamma \frac{P + {p(t)}}{V + {v(t)}}{\overset{.}{v}(t)}}} = 0.} & (4)\end{matrix}$

If the acoustic pressure levels are much less than the ambient pressurethe Equation 4 can be further simplified to Equation 5 as follows:

$\begin{matrix}{{{\overset{.}{p}(t)} + {\frac{\gamma \; P}{V}{\overset{.}{v}(t)}}} = 0.} & (5)\end{matrix}$

Using the adiabatic relation, Equation 6 can be shown as follows:

$\begin{matrix}{\frac{P}{V} = {\left( \frac{P + {p(t)}}{V + {v(t)}} \right){\left( \frac{P + {p(t)}}{P} \right)^{\frac{\gamma + 1}{\gamma}}.}}} & (6)\end{matrix}$

Thus, the error assumption is shown in Equation 7 as follows:

$\begin{matrix}{{error} = {1 - {\left( \frac{P + {p(t)}}{P} \right)^{\frac{\gamma + 1}{\gamma}}.}}} & (7)\end{matrix}$

A very loud acoustic signal (e.g., 120 dB) would correspond to pressuresine wave with amplitude of roughly 20 Pascal. Assuming air atatmospheric conditions has the parameters of γ=1.4 and P=101325 Pa, theresulting error is 0.03%. The conversion from dB to Pa is shown inEquation 8 as follows:

$\begin{matrix}{{\gamma = {20\; {\log_{10}\left( \frac{p_{rms}}{p_{ref}} \right)}}}{or}{{p_{rms} = {p_{ref}10^{\frac{\lambda}{20}}}},{where}}{p_{ref} = {20 \cdot {{\mu Pa}.}}}} & (8)\end{matrix}$

Applying the ideal gas law, P=ρRT, and substituting in for pressuregives the result as shown in Equation 9 as follows:

$\begin{matrix}{{{\overset{.}{p}(t)} + {\frac{\gamma \; {RT}\; \rho}{V}{\overset{.}{v}(t)}}} = 0.} & (9)\end{matrix}$

This can be written in terms of the speed of sound in Equation 10 asfollows:

a=√{square root over (γRT)}  (10).

And, substituting in Equation 10 in Equation 9 results in Equation 11 asfollows:

$\begin{matrix}{{{\overset{.}{p}(t)} + {\frac{\rho \; a^{2}}{V}{\overset{.}{v}(t)}}} = 0.} & (11)\end{matrix}$

Acoustic impedance for a volume is defined in Equation 12 as follows:

$\begin{matrix}{Z_{v} = {\frac{p(t)}{\overset{.}{v}(t)} = {- {\frac{1}{\left( \frac{V}{\rho \; a^{2}} \right)s}.}}}} & (12)\end{matrix}$

Modeling the Acoustic Port

The acoustic port is modeled assuming that all of the fluid in the portessentially moves as a rigid cylinder reciprocating in the axialdirection. All of the fluid in the channel is assumed to travel at thesame velocity, the channel is assumed to be of constant cross section,and the end effects resulting from the fluid entering and leaving thechannel are neglected.

If we assume laminar flow friction of the form ΔP=fρ{dot over (v)}, thefriction force acting on the mass of fluid in the channel can bewritten: F=fρA²{dot over (x)}.

A second order differential equation can then be written for thedynamics of the fluid in the channel as shown in Equation 13 as follows:

ρLA{umlaut over (x)}=ΔpA−fρA ² {dot over (x)}  (13),

or, in terms of volume flow rate as shown in Equation 14 as follows:

$\begin{matrix}{\overset{¨}{v} = {{{- \frac{fA}{L}}\overset{.}{v}} + {\Delta \; p{\frac{A}{\rho \; L}.}}}} & (14)\end{matrix}$

The acoustic impedance of the channel can then be written as shown inEquation 15:

$\begin{matrix}{Z_{p} = {\frac{\Delta \; p}{\overset{.}{v}} = {\frac{\rho \; L}{A}{\left( {s + \frac{fA}{L}} \right).}}}} & (15)\end{matrix}$

System Transfer Functions

Using the volume and port dynamics define above, the AVS system can bedescribed by the following system of Equations 16-19:

$\begin{matrix}{{{{\overset{.}{p}}_{0} - {\frac{\rho \; a^{2}}{V_{0}}{\overset{.}{v}}_{k}}} = 0},} & (16) \\{{{{\overset{.}{p}}_{1} + {\frac{\rho \; a^{2}}{V_{1}}\left( {{\overset{.}{v}}_{k} - {\overset{.}{v}}_{r}} \right)}} = 0},} & (17) \\{{{{\overset{.}{p}}_{2} + {\frac{\rho \; a^{2}}{V_{2}}{\overset{.}{v}}_{r}}} = 0},} & (18) \\{and} & \; \\{\overset{¨}{v_{r}} = {{{- \frac{fA}{L}}{\overset{.}{v}}_{r}} + {\frac{A}{\rho \; L}{\left( {p_{2} - p_{1}} \right).}}}} & (19)\end{matrix}$

One equation can be eliminated if p₀ is treated as the inputsubstituting in

${\overset{.}{v}}_{k} = {\frac{V_{0}}{\rho \; a^{2}}{\overset{.}{p}}_{0}}$

as shown in Equations 20-22:

$\begin{matrix}{{{{\overset{.}{p}}_{1} + {\frac{V_{0}}{V_{1}}{\overset{.}{p}}_{0}} - {\frac{\rho \; a^{2}}{V_{1}}{\overset{.}{v}}_{r}}} = 0},} & (20) \\{{{{\overset{.}{p}}_{2} + {\frac{\rho \; a^{2}}{V_{2}}{\overset{.}{v}}_{r}}} = 0},{and}} & (21) \\{{\overset{¨}{v}}_{r} = {{{- \frac{f\; A}{L}}{\overset{.}{v}}_{r}} + {\frac{A}{\rho \; L}p_{2}} - {\frac{A}{\rho \; L}{p_{1}.}}}} & (22)\end{matrix}$

The relationship between the two volumes on each side of the acousticport is referred to as the Cross Port transfer function. Thisrelationship is illustrated in Equation 23 as follows:

$\begin{matrix}{{{\frac{p_{2}}{p_{1}} = \frac{\omega_{n}^{2}}{s^{2} + {2\; \zeta \; \omega_{n}s} + \omega_{n}^{2}}},\mspace{14mu} {where}}{\omega_{n}^{2} = {{\frac{a^{2}A}{L}\frac{1}{V_{2}}\mspace{14mu} {and}\mspace{14mu} \zeta} = {\frac{f\; A}{2\; L\; \omega_{n}}.}}}} & (23)\end{matrix}$

This relationship has the advantage that the poles are only dependent onthe variable volume and not on the reference volume. Note that theresonant peak is actually due to the inversion of the zero in theresponse of the reference volume pressure. This means that that pressuremeasurement in the reference chamber will have a low amplitude in thevicinity of the resonance which may influence the noise in themeasurement.

Resonance Q Factor and Peak Response

The quality of the resonance is the ratio of the energy stored to thepower loss multiplied by the resonant frequency. For a pure second-ordersystem the quality factor can be expressed as a function of the dampingratio illustrated in Equation 24:

$\begin{matrix}{Q = {\frac{1}{2\zeta}.}} & (24)\end{matrix}$

The ratio of the peak response to the low-frequency response can also bewritten as a function of the damping ratio shown in Equation 25:

$\begin{matrix}{{G}_{\omega_{d}} = {\frac{1}{\zeta \sqrt{5 - {4\zeta}}}.}} & (25)\end{matrix}$

This will occur at the damped natural frequency ω_(d)=ω_(n)√{square rootover (1−ζ)}.

Electrical and Mechanical Analogies

The acoustic resonator is analogous to either a spring-mass-dampersystem or a LRC circuit, e.g., a resistor, inductor and capacitorcoupled together in series, for example.

Computing the Complex Response

To implement AVS, the system must get the relative response of the twomicrophones to the acoustic wave set up by the speaker. This isaccomplished by driving the speaker with a sinusoidal output at a knownfrequency; the complex response of each microphone is then found at thatdriving frequency. Finally, the relative responses of the twomicrophones are found and corrected for alternating sampling of theanalog-to-digital converter coupled to the processor 21 of FIG. 2.

In addition, the total signal variance is computed and compared to thevariance of pure tone extracted using the discrete Fourier transform(“DFT”). This gives a measure of how much of the signal power comes fromnoise sources or distortion. In some embodiments of the presentdisclosure, this value can be used to reject and repeat badmeasurements.

Computing the Discrete Fourier Transform

The signal from each microphone is sampled synchronously with the outputto the speaker such that a fixed number of points, N, are taken perwavelength. The measured signal at each point in the wavelength issummed over an integer number of wavelengths, M, and stored in an arrayx by an interrupt service routine (“ISR”) in the processor 21 of FIG. 2after all the data for that frequency has been collected.

A discrete Fourier transform is done on the data at the integer valuecorresponding to the driven frequency of the speaker. The generalexpression for the first harmonic of a DFT is as follows in Equation 26:

$\begin{matrix}{x_{k} = {\frac{2}{MN}{\sum\limits_{n = 0}^{N - 1}{x_{n}{e^{{- \frac{2\pi \; i}{N}}{kn}}.}}}}} & (26)\end{matrix}$

The product MN is the total number of points and the factor of 2 isadded such that the resulting real and imaginary portions of the answermatch the amplitude of the sine wave illustrated in Equation 27:

$\begin{matrix}{x_{n} = {{{{re}\left( x_{k} \right)}{\cos \left( {\frac{2\pi}{N}{kn}} \right)}} + {{{im}\left( x_{k} \right)}{{\sin \left( {\frac{2\pi}{N}{kn}} \right)}.}}}} & (27)\end{matrix}$

This real part of this expression is illustrated in Equation 28:

$\begin{matrix}{{{re}(x)} = {\frac{2}{MN}{\sum\limits_{n = 0}^{N - 1}{x_{n}{{\cos \left( {\frac{2\; \pi}{N}n} \right)}.}}}}} & (28)\end{matrix}$

We can take advantage of the symmetry of the cosine function to reducethe number of computations needed to compute the DFT. The expressionabove is equivalent to Equation 29 as follows:

$\begin{matrix}{{{re}(x)} = {{\frac{2}{MN}\left\lbrack {\left( {x_{0} - x_{\frac{1}{2}N}} \right) + {\sum\limits_{n = 1}^{{\frac{1}{4}N} - 1}{{\sin \left( {\frac{\pi}{2} - {\frac{2\; \pi}{N}n}} \right)}\left\lbrack {\left( {x_{n} - x_{{\frac{1}{2}N} + n}} \right) - \left( {x_{{\frac{1}{2}N} - n} - x_{N - n}} \right)} \right\rbrack}}} \right\rbrack}.}} & (29)\end{matrix}$

Similarly, the imaginary portion of the equation is illustrated inEquation 30 as follows:

$\begin{matrix}{{{{im}(x)} = {{- \frac{2}{MN}}{\sum\limits_{n = 0}^{N - 1}{x_{n}{\sin \left( {\frac{2\; \pi}{N}n} \right)}}}}},} & (30)\end{matrix}$

which may be expressed as Equation 31:

$\begin{matrix}{{{im}(x)} = {{\frac{2}{MN}\left\lbrack {\left( {x_{\frac{1}{4}N} - x_{\frac{3}{4}N}} \right) + {{\quad\quad}{\sum\limits_{n = 1}^{{\frac{1}{4}N} - 1}{{\sin \left( {\frac{2\; \pi}{N}n} \right)}\left\lbrack {\left( {x_{n} - x_{{\frac{1}{2}N} + n}} \right) + \left( {x_{{\frac{1}{2}N} - n} - x_{N - n}} \right)} \right\rbrack}}}} \right\rbrack}.}} & (31)\end{matrix}$

The variance of the signal at that driven frequency is illustrated inEquation 32 as follows:

σ_(tone) ²=½(re(x)²+im(x)²)   (32).

The tone variance is proportional to the acoustic power at the drivenfrequency. The maximum possible value of the real and imaginary portionsof x is 2¹¹; this corresponds to half the A/D range. The maximum valueof the tone variance is 2²¹; half the square of the AD range.

Computing the Total Signal Variance

A good measure of the integrity of a measurement is the ratio of theacoustic power at the driven frequency relative to the total acousticpower at all frequencies. The total signal variance is given by theexpression in Equation 33:

$\begin{matrix}{\sigma_{total}^{2} = {{{\frac{1}{NM}{\sum\limits_{n = 0}^{{MN} - 1}p_{n}^{2}}} - {\overset{\_}{p}}^{2}} = {{\frac{1}{NM}{\sum\limits_{n = 0}^{{MN} - 1}p_{n}^{2}}} - {\left( {\frac{1}{NM}{\sum\limits_{n = 0}^{{MN} - 1}p_{n}}} \right)^{2}.}}}} & (33)\end{matrix}$

However, in some specific embodiments, the summations are performed inthe A/D interrupt service routine (ISR) where there are time constraintsand/or all of the microphone data must be stored for post-processing. Insome embodiments, to increase efficiency, a pseudo-variance iscalculated based on a single averaged wavelength. The pseudo-variance ofthe signal is calculated using the following relation illustrated inEquation 34 as follows:

$\begin{matrix}{\sigma_{total}^{2} = {{\frac{1}{{NM}^{2}}{\sum\limits_{n = 0}^{N - 1}x_{n}^{2}}} - {\frac{1}{N^{2}M^{2}}{\left( {\sum\limits_{n = 0}^{N - 1}x_{n}} \right)^{2}.}}}} & (34)\end{matrix}$

The result is in the units of AD counts squared. The summation will beon the order of

${\sum\limits_{n = 0}^{N - 1}x_{n}^{2}} = {O\left( {{NM}^{2}2^{24}} \right)}$

for a 12-bit ADC. If N<2⁷=128 and M<2⁶=64 then the summation will beless than 2⁴³ and can be stored in a 64-bit integer. The maximumpossible value of the variance would result if the ADC oscillatedbetween a value of 0 and 2¹² on each consecutive sample. This wouldresult in a peak variance of ¼(2¹²)²=2²² so the result can be stored ata maximum of a Q9 resolution in a signed 32-bit integer.

Computing the Relative Microphone Response

The relative response of the two microphones, G, is then computed fromthe complex response of the individual microphones illustrated inEquations 35-37:

$\begin{matrix}{G = {\frac{x_{var}}{X_{ref}} = {\frac{x_{var}}{x_{ref}}{\frac{x_{ref}^{*}}{x_{ref}^{*}}.}}}} & (35) \\{{{Re}(G)} = {\frac{{{{Re}\left( x_{var} \right)}{{Re}\left( x_{ref} \right)}} + {{{Im}\left( x_{var} \right)}{{Im}\left( x_{ref} \right)}}}{{{Re}\left( x_{ref} \right)}^{2} + {{Im}\left( x_{ref} \right)}^{2}}.}} & (36) \\{{{Im}(G)} = {\frac{{{{Re}\left( x_{ref} \right)}{{Im}\left( x_{var} \right)}} - {{{Re}\left( x_{var} \right)}{{Im}\left( x_{ref} \right)}}}{{{Re}\left( x_{ref} \right)}^{2} + {{Im}\left( x_{ref} \right)}^{2}}.}} & (37)\end{matrix}$

The denominator of either expression can be expressed in terms of thereference tone variance computed in the previous section, illustrated asfollows in Equation 38:

Re(x _(ref))²+Im(x _(ref))²=2σ_(ref) ²  (38).

Correcting for A/D Skew

The speaker output may be updated at a fixed 32 times per sample. Forexample, as the driving frequency is changed, the speaker outputfrequency is also updated to maintain the fixed 32 cycles. The twomicrophones are sampled synchronous with the speaker output so thesampling frequency remains at a fixed interval of the driving frequency.The microphone A/D measurements, however, are not sampledsimultaneously; the A/D ISR alternates between the two microphones,taking a total of N samples per wavelength for each microphone. Theresult will be a phase offset between the two microphones of

$\frac{\pi}{N}.$

To correct for this phase offset, a complex rotation is applied to therelative frequency response computed in the previous section.

To rotate a complex number an angle

$\frac{\pi}{N}$

it is multiplied by

$e^{i\frac{\pi}{N}} = {{\cos \left( \frac{\pi}{N} \right)} + {i\mspace{11mu} {{\sin \left( \frac{\pi}{N} \right)}.}}}$

The result is illustrated in Equation 39 as follows:

$\begin{matrix}{G_{rotated} = {\left( {{{{Re}(G)}{\cos \left( \frac{\pi}{N} \right)}} - {{{Im}(G)}{\sin \left( \frac{\pi}{N} \right)}}} \right) + {\left( {{{{Im}(G)}{\cos \left( \frac{\pi}{N} \right)}} + {{{Re}(G)}{\sin \left( \frac{\pi}{N} \right)}}} \right){i.}}}} & (39)\end{matrix}$

Time Delays

In some embodiments, one of the assumptions when deriving the AVSequations is that the pressure is uniform in the acoustic volumes. Thisassumption is true if the acoustic wavelength is large compared to thedimensions of the AVS chamber. The wavelength of a sound wave at a givenfrequency can be computed with the following Equation 40:

$\begin{matrix}{\lambda = {\frac{a}{f}.}} & (40)\end{matrix}$

For example, the wavelength at 1 kHz is roughly 246 mm and at 5 kHz isroughly 49.2 mm. The AVS chamber may have a diameter such that the timedelay associated with acoustic waves traveling through the volumes has asmall but measurable effect. The effect can be modeled as a time delay(or time advance, depending on microphone orientation). The Laplacetransform of a pure time delay, d, is illustrated in Equation 41 asfollows:

G=e ^(ds)  (41).

The phase is influenced by the time delay, but not the magnitude ofsystem response. To correct for the time delays, the frequency responsedata may be corrected in advance by applying a model fit algorithm. Thecomplex amplitude may be rotated as a function of frequency accordingthe time delay equation above. The time delay may be assumed to befixed, so the rotation is only a function of frequency.

The time delay may be determined by running an optimization routine tofind the time delay to minimize the model fit error. Additionally oralternatively, there may be an apparent “time advance” in the data. Forexample, the reference microphone may experience a pressure perturbationslightly in advance of the acoustic port and the variable microphone mayexperience a pressure perturbation slightly behind the acoustic port.These “advances” and “delays” may be the effects of the propagation ofthe pressure waves and are in addition to “resonant” dynamics of thesystem, e.g., these effects may be accounted for.

Amplitude Leveling

The amplitude of the pressure measurements for a given speaker drivesignal may vary from device-to-device and also as a function of thedriven frequency. The device-to-device variations result frompart-to-part differences in microphone and speaker sensitivities (e.g.,roughly on the order of +/−3 dB). The frequency-based dependenciesresult from variations in speaker sensitivity over frequency as well asfrom the expected dynamics of the acoustic resonance.

To compensate, in some embodiments, the speaker gain is automaticallytuned during the AVS measurement. The speaker gains are stored in anarray with one entry for each of the sine-sweep frequencies, e.g.,within the memory 22 of FIG. 2. The amplitude of the microphone signal(from either the variable or reference microphone) may be checkedagainst the target amplitude. If it is either too large or too small abinary search routine may be employed to update the speaker gain at thatfrequency.

Checking Individual Measurement Integrity

It is possible for component errors, failures, or external disturbancesto result in an erroneous measurement. Component failures might includea distorted speaker output or failed microphone. External disturbancesmight include mechanical shock to the pump housing or an extremely loudexternal noise. These types of failures can be detected using twodifferent integrity checks: microphone saturation and out-of-bandvariance.

The microphone saturation check looks at the maximum and minimum valuesof the wavelength averaged signal for each microphone. If these valuesare close to the limits of the A/D then a flag within the processor 21of FIG. 2 is set indicating that the measurement amplitude was out ofrange.

The out-of-band variance check compares the tone variance to the totalsignal variance for each microphone. In the ideal case the ratio ofthese signals will be 1—all of the acoustic power will be at the drivenfrequency. In the event of shock or an extremely loud external acousticnoise, more power will be present at other frequencies and this valuewill be lower than unity. In some embodiments, normal operation may beconsidered to have a ratio greater than 0.99.

In some embodiments, if an individual data point fails either of theseintegrity checks, it may be repeated or excluded without having torepeat the entire sine-sweep to help facilitate AVS robustness. Otherintegrity checks may be done based on the complete sine-sweep and aredescribed later.

Volume Estimation Using Swept Sine-Generalized Solution

The resonant frequency of the system may be estimated using swept-sinesystem identification. In this method the response of the system to asinusoidal pressure variation may be found at a number of differentfrequencies. This frequency response data may be then used to estimatethe system transfer function using linear regression.

The transfer function for the system can be expressed as a rationalfunction of s. The general case is expressed below for a transferfunction with an n^(th) order numerator and an m^(th) order denominator.N and D are the coefficients for the numerator and denominatorrespectively. The equation has been normalized such that the leadingcoefficient in the denominator is 1, as illustrated in Equations 42 and43:

$\begin{matrix}{{G(s)} = \frac{{N_{n}s^{n}} + {N_{n - 1}s^{n - 1}} + \ldots + N_{0}}{s^{m} + {D_{m - 1}s^{m - 1}} + {D_{m - 2}s^{m - 2}} + \ldots + D_{0}}} & (42) \\{or} & \; \\{{G(s)} = {\frac{\sum\limits_{k = 0}^{n}\; {N_{k}s^{k}}}{s^{m} + {\sum\limits_{k = 0}^{m - 1}\; {D_{k}s^{k}}}}.}} & (43)\end{matrix}$

This equation can be re-written in the form of Equation 44 as follows:

$\begin{matrix}{{Gs}^{m} = {{\sum\limits_{k = 0}^{n}\; {N_{k}s^{k}}} - {G{\sum\limits_{k = 0}^{m - 1}\; {D_{k}{s^{k}.}}}}}} & (44)\end{matrix}$

Equation 45 shows this summation in matrix notation:

$\begin{matrix}{\begin{bmatrix}{G_{1}s_{1}^{m}} \\\vdots \\{G_{k}s_{k}^{m}}\end{bmatrix} = {{\begin{bmatrix}s_{1}^{n} & \ldots & s_{1}^{0} & {{- G_{1}}s_{1}^{m - 1}} & \ldots & {{- G_{1}}s_{1}^{0}} \\\vdots & \; & \vdots & \vdots & \; & \vdots \\s_{k}^{n} & \ldots & s_{k}^{0} & {{- G_{k}}s_{k}^{m - 1}} & \ldots & {{- G_{k}}s_{k}^{0}}\end{bmatrix}\begin{bmatrix}N_{n} \\\vdots \\N_{0} \\D_{m - 1} \\\vdots \\D_{0}\end{bmatrix}}.}} & (45)\end{matrix}$

Where k is the number of data points collected in the swept sine. Tosimplify the notation this equation can be summarized using the vectorsy illustrated in Equation 46.

y=Xc  (46).

Where y is k by 1, x is k by (m+n−1) and c is (m+n−1) by 1. Thecoefficients can then be found using a least square approach. The errorfunction can be written as shown in Equation 47:

e=y−Xc  (47).

The function to be minimized is the weighted square of the errorfunction; W is a k×k diagonal matrix, as illustrated in Equations 48-49.

e ^(T) We=(y−Xc)^(T) W(y−Xc)  (48).

e ^(T) We=y ^(T) Wy−(y ^(T) WXc)^(T) −y ^(T) WXc+c ^(T) x ^(T)WXc  (49).

The center two terms are scalars so the transpose can be neglected, asillustrated in Equations 50-52:

$\begin{matrix}{{{e^{T}{We}} = {{y^{T}{Wy}} - {2y^{T}{WXc}} + {c^{T}x^{T}{WXc}}}},} & (50) \\{{\frac{{\partial e^{T}}{We}}{\partial c} = {{{{- 2}X^{T}{Wy}} + {2X^{T}{WXc}}} = 0}},{and}} & (51) \\{c = {\left( {X^{T}{WX}} \right)^{- 1}X^{T}{{Wy}.}}} & (52)\end{matrix}$

In some embodiments, the complex transpose in all of these cases isutilized. This approach can result in complex coefficients, but theprocess can be modified to ensure that all the coefficients are real.The least-square minimization can be modified to give only realcoefficients if the error function is changed to Equation 53.

e ^(T) We=Re(y−Xc)^(T) W Re(y−Xc)+Im(y−Xc)^(T) W Im(y−Xc)  (53).

Then the coefficients can be found with the Equation 54:

c=(Re(X)^(T) W Re(X)+Im(X)^(T) W Im(X))⁻¹(Re(X)^(T) W Re(y)+Im(X)^(T) WIm(y))   (54).

Volume Estimation Using Swept Sine-Solution for a 2^(nd) Order System

For a system with a 0^(th) order numerator and a second orderdenominator as shown in the transfer function illustrated in Equation55.

$\begin{matrix}{{G(s)} = {\frac{N_{0}}{s^{2} + {D_{1}s} + D_{0}}.}} & (55)\end{matrix}$

The coefficients in this transfer function can be found based on theexpression found in the previous section as follows (Equation 56):

c=(Re(X)^(T) W Re(X)+Im(X)^(T) W Im(X))⁻¹(Re(X)^(T) W Re(y)+Im(X)^(T) WIm(y))   (56).

Where Equation 57 is as follows:

$\begin{matrix}{{y = \begin{bmatrix}{G_{1}s_{1}^{2}} \\\vdots \\{G_{k}s_{k}^{2}}\end{bmatrix}},{X = \begin{bmatrix}1 & {{- G_{1}}s_{1}} & {- G_{1}} \\\vdots & \vdots & \vdots \\1 & {{- G_{k}}s_{k}} & {- G_{k}}\end{bmatrix}},{{{and}\mspace{14mu} c} = {\begin{bmatrix}N_{0} \\D_{1} \\D_{0}\end{bmatrix}.}}} & (57)\end{matrix}$

To simplify the algorithm we can combine some of terms as illustrated inEquations 58-60:

c=D ⁻¹ b  (58),

where

D=Re(X)^(T) W Re(X)+Im(X)^(T) W Im(X)  (59),and

b=Re(X)^(T) W Re(y)+Im(X)^(T) W Im(y)  (60).

To find an expression for D in terms of the complex response vector Gand the natural frequency s=jω we first split X into its real andimaginary parts as illustrated in Equations 61 and 62, respectively, asfollows:

$\begin{matrix}{{{{Re}(X)} = \begin{bmatrix}1 & {\omega_{k}\mspace{11mu} {{Im}\left( G_{1} \right)}} & {- {{Re}\left( G_{1} \right)}} \\\vdots & \vdots & \vdots \\1 & {\omega_{k}\mspace{11mu} {{Im}\left( G_{k} \right)}} & {- {{Re}\left( G_{k} \right)}}\end{bmatrix}},{and}} & (61) \\{{{Im}(X)} = {\begin{bmatrix}0 & {{- \omega_{k}}\mspace{11mu} {{Re}\left( G_{1} \right)}} & {- {{Im}\left( G_{1} \right)}} \\\vdots & \vdots & \vdots \\0 & {{- \omega_{k}}\mspace{11mu} {{Re}\left( G_{k} \right)}} & {- {{Im}\left( G_{k} \right)}}\end{bmatrix}.}} & (62)\end{matrix}$

The real and imaginary portions of the expression for D above thenbecome Equations 63 and 64, respectively:

$\begin{matrix}{{{{{Re}(X)}^{T}W\mspace{11mu} {{Re}(X)}} = \mspace{40mu} \left\lbrack \begin{matrix}{\sum\limits_{i = 1}^{k}\; w_{i}} & {\sum\limits_{i = 1}^{k}\; {w_{i}\mspace{11mu} {{Im}\left( G_{i} \right)}\omega_{i}}} & {- {\sum\limits_{i = 1}^{k}\; {w_{i}\mspace{11mu} {{Re}\left( G_{i} \right)}}}} \\{\sum\limits_{i = 1}^{k}\; {w_{i}\mspace{11mu} {{Im}\left( G_{i} \right)}\omega_{i}}} & {\sum\limits_{i = 1}^{k}\; {w_{i}\mspace{11mu} {{Im}\left( G_{i} \right)}^{2}\omega_{i}^{2}}} & {- {\sum\limits_{i = 1}^{k}\; {w_{i}\mspace{11mu} {{Im}\left( G_{i} \right)}\; {{Re}\left( G_{i} \right)}\omega_{i}}}} \\{- {\sum\limits_{i = 1}^{k}\; {w_{i}\mspace{11mu} {{Re}\left( G_{i} \right)}}}} & {- {\sum\limits_{i = 1}^{k}\; {w_{i}\mspace{11mu} {{Im}\left( G_{i} \right)}\; {{Re}\left( G_{i} \right)}\omega_{i}}}} & {\sum\limits_{i = 1}^{k}\; {w_{i}\mspace{11mu} {{Re}\left( G_{i} \right)}^{2}}}\end{matrix} \right\rbrack},} & (63) \\{\mspace{79mu} {and}} & \; \\{{{{Im}(X)}^{T}W\mspace{11mu} {{Im}(X)}} = \mspace{140mu} {\left\lbrack \begin{matrix}0 & 0 & 0 \\0 & {\sum\limits_{i = 1}^{k}\; {w_{i}\mspace{11mu} {{Re}\left( G_{i} \right)}^{2}\omega_{i}^{2}}} & {\sum\limits_{i = 1}^{k}\; {w_{i}\mspace{11mu} {{Im}\left( G_{i} \right)}\; {{Re}\left( G_{i} \right)}\omega_{i}}} \\0 & {\sum\limits_{i = 1}^{k}\; {w_{i}\mspace{11mu} {{Im}\left( G_{i} \right)}\; {{Re}\left( G_{i} \right)}\omega_{i}}} & {\sum\limits_{i = 1}^{k}\; {w_{i}\mspace{11mu} {{Im}\left( G_{i} \right)}^{2}}}\end{matrix} \right\rbrack.}} & (64)\end{matrix}$

Combining these terms gives the final expression for the D matrix. Thismatrix will contain only real values, as shown in Equation 65 asfollows:

$\begin{matrix}{D = {\left\lbrack \begin{matrix}{\sum\limits_{i = 1}^{k}\; w_{i}} & {\sum\limits_{i = 1}^{k}\; {w_{i}\mspace{11mu} {{Im}\left( G_{i} \right)}\omega_{i}}} & {- {\sum\limits_{i = 1}^{k}\; {w_{i}\mspace{11mu} {{Re}\left( G_{i} \right)}}}} \\{\sum\limits_{i = 1}^{k}\; {w_{i}\mspace{11mu} {{Im}\left( G_{i} \right)}\omega_{i}}} & {\sum\limits_{i = 1}^{k}\; {w_{i}\mspace{11mu} \left( {{{Re}\left( G_{i} \right)}^{2} + \; {{Im}\left( G_{i} \right)}^{2}} \right)\omega_{i}^{2}}} & 0 \\{- {\sum\limits_{i = 1}^{k}\; {w_{i}\mspace{11mu} {{Re}\left( G_{i} \right)}}}} & 0 & {\sum\limits_{i = 1}^{k}\; {w_{i}\mspace{11mu} \left( {{{Re}\left( G_{i} \right)}^{2} + \; {{Im}\left( G_{i} \right)}^{2}} \right)}}\end{matrix} \right\rbrack.}} & (65)\end{matrix}$

The same approach can be taken to find an expression for the b vector interms of G and ω. The real and imaginary parts of y are illustrated inEquation 66-67.

$\begin{matrix}{{{{Re}(y)} = \begin{bmatrix}{{- {{Re}\left( G_{1} \right)}}\omega_{1}^{2}} \\\vdots \\{{- {{Re}\left( G_{k} \right)}}\omega_{k}^{2}}\end{bmatrix}},{and}} & (66) \\{{{Im}(y)} = {\begin{bmatrix}{{- {{Im}\left( G_{1} \right)}}\omega_{1}^{2}} \\\vdots \\{{- {{Im}\left( G_{k} \right)}}\omega_{k}^{2}}\end{bmatrix}.}} & (67)\end{matrix}$

Combining these two gives the expression for the b vector illustrated inEquation 68 as follows:

$\begin{matrix}{b = {{{{{Re}(X)}^{T}W\mspace{14mu} {{Re}(y)}} + {{{Im}(X)}^{T}W\mspace{14mu} {{Im}(y)}}} = {\begin{bmatrix}{- {\sum\limits_{i = 1}^{k}{w_{i}{{Re}\left( G_{i} \right)}\omega_{i}^{2}}}} \\0 \\{\sum\limits_{i = 1}^{k}{{w_{i}\left( {{{Re}\left( G_{i} \right)}^{2} + {{Im}\left( G_{i} \right)}^{2}} \right)}\omega_{i}^{2}}}\end{bmatrix}.}}} & (68)\end{matrix}$

The next step is to invert the D matrix. The matrix is symmetric andpositive-definite so the number of computations needed to find theinverse will be reduced from the general 3×3 case. The generalexpression for a matrix inverse is shown in Equation 69 as:

$\begin{matrix}{D^{- 1} = {\frac{1}{\det (D)}{{{adj}(D)}.}}} & (69)\end{matrix}$

If D is expressed as in Equation 70:

$\begin{matrix}{{D = \begin{bmatrix}d_{11} & d_{12} & d_{13} \\d_{12} & d_{22} & 0 \\d_{13} & 0 & d_{33}\end{bmatrix}},} & (70)\end{matrix}$

then the adjugate matrix can be written as in Equation 71 as follows:

$\begin{matrix}{{{adj}(D)} = {\quad{\left\lbrack {- \begin{matrix}{\begin{matrix}d_{22} & 0 \\0 & d_{33}\end{matrix}} & {- {\begin{matrix}d_{12} & 0 \\d_{13} & d_{33}\end{matrix}}} & {\begin{matrix}d_{12} & d_{22} \\d_{13} & 0\end{matrix}} \\{\begin{matrix}d_{12} & d_{13} \\0 & d_{33}\end{matrix}} & {\begin{matrix}d_{11} & d_{13} \\d_{13} & d_{33}\end{matrix}} & {- {\begin{matrix}d_{11} & d_{12} \\d_{13} & 0\end{matrix}}} \\{\begin{matrix}d_{12} & d_{13} \\d_{22} & 0\end{matrix}} & {- {\begin{matrix}d_{11} & d_{13} \\d_{12} & 0\end{matrix}}} & {\begin{matrix}d_{11} & d_{12} \\d_{12} & d_{22}\end{matrix}}\end{matrix}} \right\rbrack = {\left\lbrack \begin{matrix}a_{11} & a_{12} & a_{13} \\a_{12} & a_{22} & a_{23} \\a_{13} & a_{32} & a_{33}\end{matrix} \right\rbrack .}}}} & (71)\end{matrix}$

Due to symmetry, only the upper diagonal matrix needs to be calculated.The Determinant can then be computed in terms of the adjugate matrixvalues, taking advantage of the zero elements in the original array asillustrated in Equation 72 as follows:

det(D)=a ₁₂ d ₁₂ +a ₂₂ d ₂₂  (72).

Finally, the inverse of D can be written in the form shown in Equation73:

$\begin{matrix}{D^{- 1} = {\frac{1}{\det (D)}{{{adj}(D)}.}}} & (73)\end{matrix}$

In some embodiments, we may solve the value in Equation 74:

$\begin{matrix}{{c = {{D^{- 1}b} = {\frac{1}{\det (D)}{{adj}(D)}b}}};} & (74)\end{matrix}$

So that Equation (75) is used:

$\begin{matrix}{{c = {{{\frac{1}{\det (D)}\left\lbrack \begin{matrix}a_{11} & a_{12} & a_{13} \\a_{12} & a_{22} & a_{23} \\a_{13} & a_{32} & a_{33}\end{matrix} \right\rbrack}\begin{bmatrix}b_{1} \\0 \\b_{3}\end{bmatrix}} = {\frac{1}{\det (D)}\left\lbrack \begin{matrix}{{a_{11}b_{1}} + {a_{13}b_{3}}} \\{{a_{12}b_{1}} + {a_{23}b_{3}}} \\{{a_{13}b_{1}} + {a_{33}b_{3}}}\end{matrix} \right\rbrack}}},} & (75)\end{matrix}$

To get a quantitative assessment of how well the data fits the model,the original expression for the error as shown in Equation 76 isutilized:

e ^(T) We=Re(y−Xc)^(T) W Re(y−Xc)+Im(y−Xc)^(T) W Im(y−Xc)  (76).

This can be expressed in terms of the D matrix and the b and c vectorsillustrated in Equation 77:

e ^(T) We=h−2c ^(T) b+c ^(T) Dc  (77),

where:

h=Re(y ^(T))W Re(y)+Im(y ^(T))W Im(y)  (78), and

$\begin{matrix}{h = {\sum\limits_{i = 1}^{k}{{w_{i}\left( {{{Re}\left( G_{i} \right)}^{2} + {{Im}\left( G_{i} \right)}^{2}} \right)}{\omega_{i}^{4}.}}}} & (79)\end{matrix}$

In some embodiments, to compare the errors from different sine sweeps,the fit error is normalized by the square of the weighted by matrix asfollows in Equation 80, where h is a scalar:

e ^(T) Weh ⁻¹=(h−2c ^(T) b+c ^(T) Dc)h ⁻¹  (80).

Volume Estimation Using Swept Sine-Estimating Volume

The model fit may be used such that the resonant frequency of the portmay be extracted from the sine sweep data. The delivered volume may berelated to this value. The ideal relationship between the two can beexpressed by the relation illustrated in Equation 81:

$\begin{matrix}{\omega_{n}^{2} = {\frac{a^{2}A}{L}{\frac{1}{V_{2}}.}}} & (81)\end{matrix}$

The speed of sound will vary with the temperature, so it is useful tosplit out the temperature effects as shown in Equation 82:

$\begin{matrix}{\omega_{n}^{2} = {\frac{\gamma \; {RA}}{L}{\frac{T}{V_{2}}.}}} & (82)\end{matrix}$

The volume can then be expressed as a function of the measured resonantfrequency and the temperature, illustrated in Equation 83 as follows:

$\begin{matrix}{V_{2} = {C{\frac{T}{\omega_{n}^{2}}.}}} & (83)\end{matrix}$

Where C is the calibration constant illustrated in Equation 84 asfollows:

$\begin{matrix}{C = {\frac{\gamma \; {RA}}{L}.}} & (84)\end{matrix}$

Volume Estimation Using Swept Sine-Volume Estimation Integrity Checks

In some embodiments, a second set of integrity check can be performedout of the output of the mode fit and volume estimation routines (thefirst set of checks is done at the FFT level). Checks may be done eitherthrough redundancy or through range checking for several values, suchas: (1) model fit error, (2) estimated damping ratio, (3) estimatedtransfer function gain, (4) estimated natural frequency, (5) estimatedvariable volume, and (6) AVS sensor temperature.

In addition, portions of the AVS calculations may be done redundantly onthe processor 21 of FIG. 2 using an independent temperature sensor andan independent copy of the calibration parameters to guard against RAMfailures, in some specific embodiments.

Volume Estimation Using Swept Sine-Disposable Detection

The presence of the disposable, e.g., cartridges or reservoirs that areattachable, may be detected using a magnetic switch and mechanicalinterlock, in some specific embodiments. However, a second detectionmethod may be used to 1) differentiate between the pump being attachedto a disposable and a charger, and 2) provide a backup to the primarydetection methods.

If the disposable is not present, the variable volume, V₂, iseffectively very large. As a result, there will be a normal signal fromthe reference microphone, but there will be very little signal on thevariable microphones. If the mean amplitude of the reference microphoneduring a sine sweep is normal (this verifies that the speaker isworking) and the mean amplitude of the variable microphone is small, aflag is set in the processor 21 of FIG. 2 indicating that the disposableis not present.

Implementation Details—Sizing V1 Relative to V2

Sizing V₁ may include trading off acoustic volume with the relativeposition of the poles and zeros in the transfer function. The transferfunction for both V₁ and V₂ are shown below relative to the volumedisplacement of the speaker as illustrated in Equations 85-88, asfollows:

$\begin{matrix}{{\frac{p_{2}}{v_{k}} = {{- \frac{\rho \; a^{2}}{V_{1}}}\frac{\omega_{n}^{2}}{s^{2} + {2\; \zeta \; \omega_{n}s} + {\alpha\omega}_{n}^{2}}}},{and}} & (85) \\{{\frac{p_{1}}{v_{k}} = {{- \frac{\rho \; a^{2}}{V_{1}}}\frac{s^{2} + {2\; \zeta \; \omega_{n}s} + {\alpha\omega}_{n}^{2}}{s^{2} + {2\; \zeta \; \omega_{n}s} + \omega_{n}^{2}}}},{where}} & (86) \\{{\omega_{n}^{2} = {\frac{a^{2}A}{L}\frac{1}{V_{2}}}},{\zeta = {\frac{f\; A}{2\; L\; \omega_{n}}\mspace{20mu} {and}}}} & (87) \\{\alpha = {\left( {1 + \frac{V_{2}}{V_{1}}} \right).}} & (88)\end{matrix}$

As V₁ is increased the gain decreases and the speaker must be driven ata higher amplitude to get the same sound pressure level. However,increasing V₁ has the benefit of moving the complex zeros in the p₁transfer function toward the complex poles. In the limiting case whereV₁→∞ then α→1 and you have pole-zero cancellation and a flat response.Increasing V₁, therefore, has the reduces both the resonance and thenotch in the p₁ transfer function, and moves the p₂ poles toward ω_(n);the result is a lower sensitivity to measurement error when calculatingthe p₂/p₁ transfer function.

Implementation Details—Aliasing

Higher frequencies can alias down to the frequency of interest. Thealiased frequency can be expressed in Equation 89 as follows:

f=|f _(n) −nf _(s)|  (89).

Where f_(s) is the sampling frequency, f_(n) is the frequency of thenoise source, n is a positive integer, and f is the aliased frequency ofthe noise source.

The demodulation routine may filter out noise except at the specificfrequency of the demodulation. If the sample frequency is setdynamically to be a fixed multiple of the demodulation frequency, thenthe frequency of the noise that can alias down to the demodulationfrequency will be a fixed set of harmonics of that fundamentalfrequency.

For example, if the sampling frequency is 8 times the demodulationfrequency then the noise frequencies that can alias down to thatfrequency are

$\begin{matrix}{{\frac{f_{n}}{f} = {\left\{ {\frac{1}{{n\; \beta} + 1},\frac{1}{{n\; \beta} - 1}} \right\} = \left\{ {\frac{1}{7},\frac{1}{9},\frac{1}{15},\frac{1}{17},\frac{1}{23},\frac{1}{25},{.\;.\;.}}\mspace{14mu} \right\}}}} & (90) \\{{{where}\mspace{14mu} \beta} = {\frac{f_{s}}{f} = 8.}} & (91)\end{matrix}$

For β=16 we would have the series

$\begin{matrix}{\frac{f_{n}}{f} = \left\{ {\frac{1}{15},\frac{1}{17},\frac{1}{31},\frac{1}{33},{.\;.\;.}}\mspace{14mu} \right\}} & (92)\end{matrix}$

Sources of Avs Measurement Error—Avs Chamber Movement

In some embodiments, one of the assumptions of the AVS measurement isthat the total AVS volume (V₂ plus the volume taken up the by the othercomponents) is constant. However, if the AVS housing flexes the totalvolume of the AVS chamber may change slightly and affect thedifferential volume measurement. In some embodiments, to keep thecontribution of the volume error is kept to be less than 1.0% of thefluid delivery.

Sources of Avs Measurement Error—External Noise

In some embodiments, external noise sources may be filtered out.

Sources of Avs Measurement Error—Mechanical Shock

Mechanical shock to the pump housing during an AVS measurement willaffect the microphone measurements and may result in an error in thefrequency response data. This error, however, is detectable using theout-of-band variance check in the demodulation routine by the processor21 of FIG. 2. If such an error is detected, the data point can berepeated (e.g., another sample is taken) resulting in little or noeffect on the resulting AVS measurement.

Sources of Avs Measurement Error—Air in the AVS Chamber

A mechanism for an air bubble to affect the AVS measurement is through asecondary resonance. This secondary resonance will make the system 4thorder and, depending on the frequency and magnitude of the secondaryresonance, can cause some error if the estimation is using a 2^(nd)order model.

Sources of Avs Measurement Error—Electrical Component Failure

In general, failure an electrical component will result in no signal orin increased harmonic distortion. In either case the fault would bedetected by AVS integrity checks and the measurement invalidated.

The one exception that has been identified is a failure of theoscillator used to control the DAC and ADC. If this oscillator were todrift out of tolerance it would introduce a measurement error that wouldnot be detected by the low-level integrity check (it would be detectedin an extreme case by the volume integrity checks described above). Toguard against these failures, in some embodiments, the oscillator ischecked against an independent clock whenever an AVS measurement isinitiated.

What is claimed is:
 1. A pump, comprising: a reservoir configured todeliver a fluid; a port coupled to the reservoir and configured todischarge the fluid; a plunger having a piston coupled to a shaft,wherein the piston is disposed within the reservoir in slidingengagement with an inner surface of the reservoir, wherein the pistondefines a first side of the reservoir and a second side of the reservoirwhereby movement of the plunger towards the first side of the reservoirdischarges fluid through the port; and a reference-volume assemblycoupled to the reservoir, wherein the reference-volume assemblycomprises: a reference-volume chamber in acoustic communication with thesecond side of the reservoir; a speaker disposed within thereference-volume chamber; and a reference microphone disposed within thereference-volume chamber, wherein the reference-volume assembly furthercomprises a conduit configured to receive the shaft, wherein the shaftis in sliding engagement with the conduit.
 2. The pump according toclaim 1, wherein the reference-volume assembly is coupled to thereservoir at an opposite end of the reservoir relative to the port. 3.The pump according to claim 2, further comprising a variable-volumemicrophone disposed within the reservoir configured to sense a soundwave within the reservoir, the sound wave originating from the speaker.4. The pump according to claim 1, further comprising: an additionalreservoir configured to deliver an additional fluid; an additional portcoupled to the additional reservoir and configured to discharge theadditional fluid; and an additional plunger having an additional pistoncoupled to an additional shaft, wherein the additional piston isdisposed within the additional reservoir in sliding engagement with aninner surface of the additional reservoir, wherein the additional pistondefines a first side of the additional reservoir and a second side ofthe additional reservoir whereby movement of the additional plungertowards the first side of the additional reservoir discharges fluidthrough the additional port; wherein the reference-volume assembly isfurther coupled to the additional reservoir at an opposite end of theadditional reservoir relative to the additional port, wherein thereference-volume chamber is further in acoustic communication with thesecond side of the additional reservoir.
 5. The pump according to claim4, wherein at least one of the first and second reservoirs areattachable to the reference-volume assembly.
 6. The pump according toclaim 5, further comprising a manifold, the manifold comprising: a firstconnector port coupled to the port; a second connector port coupled tothe additional port; a discharge port; and a fluid path fluidlyconnecting together the first and second connector ports to thedischarge port.
 7. The pump according to claim 6, wherein the manifoldis attachable to the first and second connector ports.
 8. The pumpaccording to claim 4, further comprising a variable-volume microphonedisposed within the reservoir configured to sense a sound wave withinthe reservoir.
 9. The pump according to claim 8, further comprising anadditional variable-volume microphone disposed within the additionalreservoir configured to sense the sound wave within the additionalreservoir.
 10. The pump according to claim 4, further comprising avariable-volume microphone disposed on the reference-volume assemblyconfigured to sense a sound wave within the reservoir.
 11. The pumpaccording to claim 10, further comprising an additional variable-volumemicrophone disposed on the reference-volume assembly configured to sensethe sound wave within the additional reservoir.
 12. The pump accordingto claim 1, further comprising: a linear position sensor configured tosense a position of the shaft.
 13. The pump according to claim 1,further comprising a housing, wherein the reservoir is disposed withinthe housing; and wherein the plunger is disposed within the housing. 14.The pump according to claim 1, further comprising an actuator coupled tothe shaft to actuate the plunger.
 15. The pump according to claim 14,further comprising a housing, wherein the actuator is disposed withinthe housing.
 16. The pump according to claim 12, further comprising ahousing, wherein the linear position sensor is disposed within thehousing.
 17. The pump according to claim 1, wherein the piston comprisesa seal disposed along a periphery of the piston.
 18. The pump accordingto claim 1, wherein the plunger is moveable between a fully dischargedposition and a fully loaded position, wherein the reference-volumechamber is in fluid communication with the second side of the reservoirwhen the plunger is positioned anywhere between the fully dischargedposition and the fully loaded position.
 19. The pump according to claim1, wherein the conduit further comprises a seal configured to receivethe shaft and acoustically seal the second side of the reservoir as theshaft engages with the conduit.
 20. The pump according to claim 1,wherein the reference-volume assembly further comprises an acoustic portin acoustic communication with the reference-volume chamber and thesecond side of the reservoir.